9608 Difference Equations Fibonacci

1) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 6?

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, the first term is 1 and the second term is 3. To find the value of term number 6, we need to calculate the next four terms in the sequence. The third term is 1 + 3 = 4, the fourth term is 3 + 4 = 7, the fifth term is 4 + 7 = 11, and the sixth term is 7 + 11 = 18. Therefore, the value of term number 6 is 18.

Explanation

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, the first term is 1 and the second term is 3. To find the value of term number 6, we need to calculate the next four terms in the sequence. The third term is 1 + 3 = 4, the fourth term is 3 + 4 = 7, the fifth term is 4 + 7 = 11, and the sixth term is 7 + 11 = 18. Therefore, the value of term number 6 is 18.

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2) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 7?

The Lucas sequence is a series of numbers in which each term is the sum of the two preceding terms. In this case, the first term (t1) is 1 and the second term (t2) is 3. To find the value of term number 7, we need to calculate the sum of the 6th and 5th terms. By following the pattern, we can determine that the 6th term is 18 (3 + 15) and the 5th term is 11 (15 - 4). Therefore, the value of term number 7 is 29 (18 + 11).

Explanation

The Lucas sequence is a series of numbers in which each term is the sum of the two preceding terms. In this case, the first term (t1) is 1 and the second term (t2) is 3. To find the value of term number 7, we need to calculate the sum of the 6th and 5th terms. By following the pattern, we can determine that the 6th term is 18 (3 + 15) and the 5th term is 11 (15 - 4). Therefore, the value of term number 7 is 29 (18 + 11).

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3)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given explanation states that the provided equation is not a second order difference equation. However, the explanation does not provide any specific reasons or evidence to support this claim. Therefore, it is difficult to fully understand the reasoning behind this answer without further context or information.

Explanation

The given explanation states that the provided equation is not a second order difference equation. However, the explanation does not provide any specific reasons or evidence to support this claim. Therefore, it is difficult to fully understand the reasoning behind this answer without further context or information.

4) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 8?

The Lucas sequence starts with t1 = 1 and t2 = 3. Each term in the sequence is the sum of the previous two terms. To find the value of term number 8, we need to calculate the sequence up to that point. The sequence would be: 1, 3, 4, 7, 11, 18, 29, 47. Therefore, the value of term number 8 is 47.

Explanation

The Lucas sequence starts with t1 = 1 and t2 = 3. Each term in the sequence is the sum of the previous two terms. To find the value of term number 8, we need to calculate the sequence up to that point. The sequence would be: 1, 3, 4, 7, 11, 18, 29, 47. Therefore, the value of term number 8 is 47.

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5) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 9?

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, the first term (t1) is 1 and the second term (t2) is 3. To find the value of term number 9, we need to calculate the sequence up to that point. By adding the previous two terms (3+1=4), we get the third term. Continuing this pattern, we can calculate the subsequent terms until we reach the ninth term, which is 76.

Explanation

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, the first term (t1) is 1 and the second term (t2) is 3. To find the value of term number 9, we need to calculate the sequence up to that point. By adding the previous two terms (3+1=4), we get the third term. Continuing this pattern, we can calculate the subsequent terms until we reach the ninth term, which is 76.

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6)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given statement is not a second order difference equation because it does not involve the second order difference of the sequence. A second order difference equation would involve the differences between consecutive terms and the differences between those differences. In this case, the statement does not provide any information about the differences between the differences, indicating that it is not a second order difference equation.

Explanation

The given statement is not a second order difference equation because it does not involve the second order difference of the sequence. A second order difference equation would involve the differences between consecutive terms and the differences between those differences. In this case, the statement does not provide any information about the differences between the differences, indicating that it is not a second order difference equation.

7) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 10?

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. Starting with t1 = 1 and t2 = 3, we can calculate the sequence as follows: t3 = t1 + t2 = 1 + 3 = 4, t4 = t2 + t3 = 3 + 4 = 7, t5 = t3 + t4 = 4 + 7 = 11, and so on. The value of term number 10 in the Lucas sequence is 123.

Explanation

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. Starting with t1 = 1 and t2 = 3, we can calculate the sequence as follows: t3 = t1 + t2 = 1 + 3 = 4, t4 = t2 + t3 = 3 + 4 = 7, t5 = t3 + t4 = 4 + 7 = 11, and so on. The value of term number 10 in the Lucas sequence is 123.

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8)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given answer states that the equation is not a second order difference equation. This means that the equation does not involve the difference between two consecutive terms, but rather involves the difference between terms that are further apart. In a second order difference equation, the difference between terms is taken twice. Since the equation in question does not follow this pattern, it is not a second order difference equation.

Explanation

The given answer states that the equation is not a second order difference equation. This means that the equation does not involve the difference between two consecutive terms, but rather involves the difference between terms that are further apart. In a second order difference equation, the difference between terms is taken twice. Since the equation in question does not follow this pattern, it is not a second order difference equation.

9) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 11?

The Lucas sequence is a sequence of numbers where each term is the sum of the previous two terms. In this case, the first term is 1 and the second term is 3. To find the value of term number 11, we can calculate the sequence by adding the previous two terms. By doing this, we can determine that the value of term number 11 is 199.

Explanation

The Lucas sequence is a sequence of numbers where each term is the sum of the previous two terms. In this case, the first term is 1 and the second term is 3. To find the value of term number 11, we can calculate the sequence by adding the previous two terms. By doing this, we can determine that the value of term number 11 is 199.

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10)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given answer states that the equation is not a second order difference equation. This means that the equation does not involve the difference of the second order terms. It could be a first order or higher order difference equation, but it is not specifically a second order difference equation.

Explanation

The given answer states that the equation is not a second order difference equation. This means that the equation does not involve the difference of the second order terms. It could be a first order or higher order difference equation, but it is not specifically a second order difference equation.

11) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 12?

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, the first term (t1) is 1 and the second term (t2) is 3. To find the value of the 12th term, we need to continue adding the previous two terms until we reach the desired term. By following this pattern, we find that the 12th term is 322.

Explanation

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, the first term (t1) is 1 and the second term (t2) is 3. To find the value of the 12th term, we need to continue adding the previous two terms until we reach the desired term. By following this pattern, we find that the 12th term is 322.

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12)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given statement suggests that the equation provided does not meet the criteria for a second order difference equation. It implies that the equation does not involve the differences between consecutive terms, as expected in a second order difference equation. Therefore, the equation does not fit the definition of a second order difference equation.

Explanation

The given statement suggests that the equation provided does not meet the criteria for a second order difference equation. It implies that the equation does not involve the differences between consecutive terms, as expected in a second order difference equation. Therefore, the equation does not fit the definition of a second order difference equation.

13) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 1?

The value of term number 1 in the Fibonacci-Type sequence is 2.

Explanation

The value of term number 1 in the Fibonacci-Type sequence is 2.

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14)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given answer states that the equation is not a second order difference equation. This means that the equation does not involve the differences of the terms up to the second order. It could be a first order difference equation or a higher order difference equation, but it is not a second order difference equation.

Explanation

The given answer states that the equation is not a second order difference equation. This means that the equation does not involve the differences of the terms up to the second order. It could be a first order difference equation or a higher order difference equation, but it is not a second order difference equation.

15) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 2?

The Fibonacci-Type sequence is a sequence of numbers where each number is the sum of the two preceding ones. In this case, the first term (t1) is 2 and the second term (t2) is 3. To find the value of term number 2, we can directly look at t2, which is 3. Therefore, the value of term number 2 is 3.

Explanation

The Fibonacci-Type sequence is a sequence of numbers where each number is the sum of the two preceding ones. In this case, the first term (t1) is 2 and the second term (t2) is 3. To find the value of term number 2, we can directly look at t2, which is 3. Therefore, the value of term number 2 is 3.

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16) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 3?

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t1 = 2 and t2 = 3, we can calculate the value of term number 3 by adding t1 and t2 together. Therefore, the value of term number 3 is 5.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t1 = 2 and t2 = 3, we can calculate the value of term number 3 by adding t1 and t2 together. Therefore, the value of term number 3 is 5.

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17) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 4?

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t1 = 2 and t2 = 3, we can calculate the value of term number 4 by adding the preceding two terms: 2 + 3 = 5. Therefore, the value of term number 4 is 5.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t1 = 2 and t2 = 3, we can calculate the value of term number 4 by adding the preceding two terms: 2 + 3 = 5. Therefore, the value of term number 4 is 5.

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18)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given answer states that the equation is not a second order difference equation. This means that the equation does not involve a difference of differences, which is a characteristic of a second order difference equation. Therefore, the equation in question does not fit the criteria for being a second order difference equation.

Explanation

The given answer states that the equation is not a second order difference equation. This means that the equation does not involve a difference of differences, which is a characteristic of a second order difference equation. Therefore, the equation in question does not fit the criteria for being a second order difference equation.

19) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 5?

The Fibonacci-Type sequence starts with t1 = 2 and t2 = 3. Each term in the sequence is the sum of the previous two terms. Therefore, t3 = 2 + 3 = 5, t4 = 3 + 5 = 8, and t5 = 5 + 8 = 13. Thus, the value of term number 5 is 13.

Explanation

The Fibonacci-Type sequence starts with t1 = 2 and t2 = 3. Each term in the sequence is the sum of the previous two terms. Therefore, t3 = 2 + 3 = 5, t4 = 3 + 5 = 8, and t5 = 5 + 8 = 13. Thus, the value of term number 5 is 13.

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20)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given difference equation does not have the form of a second order difference equation. A second order difference equation typically involves the difference of two consecutive terms and the difference of two terms before that. However, the given equation does not involve such differences and hence cannot be classified as a second order difference equation.

Explanation

The given difference equation does not have the form of a second order difference equation. A second order difference equation typically involves the difference of two consecutive terms and the difference of two terms before that. However, the given equation does not involve such differences and hence cannot be classified as a second order difference equation.

21) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 6?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, t1 is 2 and t2 is 3. To find the value of term number 6, we need to calculate the sequence up to that point. The sequence would be: 2, 3, 5, 8, 13, 21. Therefore, the value of term number 6 is 21.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, t1 is 2 and t2 is 3. To find the value of term number 6, we need to calculate the sequence up to that point. The sequence would be: 2, 3, 5, 8, 13, 21. Therefore, the value of term number 6 is 21.

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22)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given statement suggests that the equation provided is not a second order difference equation. A second order difference equation is a mathematical equation that relates the values of a sequence to the differences between consecutive terms. However, the statement does not provide any specific information about the equation or its characteristics, making it difficult to provide a more detailed explanation.

Explanation

The given statement suggests that the equation provided is not a second order difference equation. A second order difference equation is a mathematical equation that relates the values of a sequence to the differences between consecutive terms. However, the statement does not provide any specific information about the equation or its characteristics, making it difficult to provide a more detailed explanation.

23) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 7?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, t1 is given as 2 and t2 is given as 3. To find the value of term number 7, we can use the formula: tn = tn-1 + tn-2. By applying this formula repeatedly, we can calculate the sequence as follows: t3 = 2 + 3 = 5, t4 = 3 + 5 = 8, t5 = 5 + 8 = 13, t6 = 8 + 13 = 21, t7 = 13 + 21 = 34. Therefore, the value of term number 7 is 34.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, t1 is given as 2 and t2 is given as 3. To find the value of term number 7, we can use the formula: tn = tn-1 + tn-2. By applying this formula repeatedly, we can calculate the sequence as follows: t3 = 2 + 3 = 5, t4 = 3 + 5 = 8, t5 = 5 + 8 = 13, t6 = 8 + 13 = 21, t7 = 13 + 21 = 34. Therefore, the value of term number 7 is 34.

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24) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 8?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, the sequence starts with t1 = 2 and t2 = 3. To find the value of term number 8, we need to continue the sequence by adding the previous two terms. By doing so, we get the following sequence: 2, 3, 5, 8, 13, 21, 34, 55. Therefore, the value of term number 8 is 55.

Explanation

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, the sequence starts with t1 = 2 and t2 = 3. To find the value of term number 8, we need to continue the sequence by adding the previous two terms. By doing so, we get the following sequence: 2, 3, 5, 8, 13, 21, 34, 55. Therefore, the value of term number 8 is 55.

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25) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 9?

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t1 = 2 and t2 = 3, we can find the value of term number 9 by continuously adding the previous two terms. Starting with t3 = 2 + 3 = 5, we can continue this process until we reach term number 9. The sequence would be: 2, 3, 5, 8, 13, 21, 34, 55, and finally, 89. Therefore, the value of term number 9 is 89.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t1 = 2 and t2 = 3, we can find the value of term number 9 by continuously adding the previous two terms. Starting with t3 = 2 + 3 = 5, we can continue this process until we reach term number 9. The sequence would be: 2, 3, 5, 8, 13, 21, 34, 55, and finally, 89. Therefore, the value of term number 9 is 89.

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26) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 10?

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, the sequence starts with t1 = 2 and t2 = 3. To find the value of term number 10, we need to continue adding the preceding two numbers until we reach the 10th term. By following this pattern, the 10th term of the Fibonacci sequence is 144.

Explanation

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, the sequence starts with t1 = 2 and t2 = 3. To find the value of term number 10, we need to continue adding the preceding two numbers until we reach the 10th term. By following this pattern, the 10th term of the Fibonacci sequence is 144.

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27) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 11?

The Fibonacci-Type sequence starts with 2 and 3, and each subsequent term is the sum of the two previous terms. To find the value of term number 11, we need to calculate the sequence up to that point. Starting with t1 = 2 and t2 = 3, we add them together to get t3 = 5. Continuing this pattern, we get t4 = 8, t5 = 13, t6 = 21, t7 = 34, t8 = 55, t9 = 89, t10 = 144, and finally t11 = 233. Therefore, the value of term number 11 is 233.

Explanation

The Fibonacci-Type sequence starts with 2 and 3, and each subsequent term is the sum of the two previous terms. To find the value of term number 11, we need to calculate the sequence up to that point. Starting with t1 = 2 and t2 = 3, we add them together to get t3 = 5. Continuing this pattern, we get t4 = 8, t5 = 13, t6 = 21, t7 = 34, t8 = 55, t9 = 89, t10 = 144, and finally t11 = 233. Therefore, the value of term number 11 is 233.

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28) From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 12?

The Fibonacci-Type sequence starts with t1 = 2 and t2 = 3. Each subsequent term is the sum of the two previous terms. To find the value of term number 12, we can use the formula: tn = tn-1 + tn-2. By applying this formula repeatedly, we can calculate the values of the sequence until we reach term number 12, which is equal to 377.

Explanation

The Fibonacci-Type sequence starts with t1 = 2 and t2 = 3. Each subsequent term is the sum of the two previous terms. To find the value of term number 12, we can use the formula: tn = tn-1 + tn-2. By applying this formula repeatedly, we can calculate the values of the sequence until we reach term number 12, which is equal to 377.

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29) From the Fibonacci-Type sequence, where t5 = 3 AND t6 = 8, what is the value of t4?

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t5 is 3 and t6 is 8, we can determine the value of t4 by subtracting t5 from t6. Therefore, t4 is equal to 8 - 3, which is 5.

Explanation

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t5 is 3 and t6 is 8, we can determine the value of t4 by subtracting t5 from t6. Therefore, t4 is equal to 8 - 3, which is 5.

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30) From the Fibonacci-Type sequence, where t6 = 5 AND t7 = 12, what is the value of t5?

The Fibonacci-Type sequence is a sequence where each number is the sum of the two preceding ones. In this case, t6 is the sum of t4 and t5, and t7 is the sum of t5 and t6. Given that t6 is 5 and t7 is 12, we can deduce that t4 is 5 - t5 and t5 is 12 - t6. By substituting the values, we find that t5 is equal to 7.

Explanation

The Fibonacci-Type sequence is a sequence where each number is the sum of the two preceding ones. In this case, t6 is the sum of t4 and t5, and t7 is the sum of t5 and t6. Given that t6 is 5 and t7 is 12, we can deduce that t4 is 5 - t5 and t5 is 12 - t6. By substituting the values, we find that t5 is equal to 7.

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31) From the Fibonacci-Type sequence, where t7 = 7 AND t8 = 16, what is the value of t6?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, t7 = 7 and t8 = 16. To find the value of t6, we need to determine the sum of t5 and t4. Since t7 is 7 and t8 is 16, we can deduce that t6 must be the difference between t8 and t7, which is 16 - 7 = 9. Therefore, the value of t6 is 9.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, t7 = 7 and t8 = 16. To find the value of t6, we need to determine the sum of t5 and t4. Since t7 is 7 and t8 is 16, we can deduce that t6 must be the difference between t8 and t7, which is 16 - 7 = 9. Therefore, the value of t6 is 9.

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32) From the Fibonacci-Type sequence, where t8 = 9 AND t9 = 20, what is the value of t7?

In a Fibonacci-Type sequence, each term is the sum of the two previous terms. Therefore, to find the value of t7, we need to subtract the value of t8 from t9. Since t8 = 9 and t9 = 20, the difference between them is 11. Therefore, the value of t7 is 11.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the two previous terms. Therefore, to find the value of t7, we need to subtract the value of t8 from t9. Since t8 = 9 and t9 = 20, the difference between them is 11. Therefore, the value of t7 is 11.

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34) From the Fibonacci-Type sequence, where t10 = 13 AND t11 = 28, what is the value of t9?

Based on the given information that t10 = 13 and t11 = 28 in the Fibonacci-Type sequence, we can determine the value of t9. In the Fibonacci sequence, each term is the sum of the two preceding terms. Therefore, to find t9, we need to subtract t10 from t11. Since t11 = 28 and t10 = 13, subtracting t10 from t11 gives us 28 - 13 = 15. Hence, the value of t9 is 15.

Explanation

Based on the given information that t10 = 13 and t11 = 28 in the Fibonacci-Type sequence, we can determine the value of t9. In the Fibonacci sequence, each term is the sum of the two preceding terms. Therefore, to find t9, we need to subtract t10 from t11. Since t11 = 28 and t10 = 13, subtracting t10 from t11 gives us 28 - 13 = 15. Hence, the value of t9 is 15.

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35) From the Fibonacci-Type sequence, where t11 = 15 AND t12 = 32, what is the value of t10?

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. To find t10, we need to find the sum of t9 and t8. Since t11 is given as 15 and t12 is given as 32, we can find t9 by subtracting t12 from t11 (15 - 32 = -17) and t8 by subtracting t11 from t12 (32 - 15 = 17). Therefore, the value of t10 is 17.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. To find t10, we need to find the sum of t9 and t8. Since t11 is given as 15 and t12 is given as 32, we can find t9 by subtracting t12 from t11 (15 - 32 = -17) and t8 by subtracting t11 from t12 (32 - 15 = 17). Therefore, the value of t10 is 17.

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36) From the Fibonacci-Type sequence, where t12 = 17 AND t13 = 36, what is the value of t11?

In a Fibonacci-type sequence, each term is the sum of the previous two terms. Therefore, to find the value of t11, we need to subtract the value of t13 (36) from the value of t12 (17) to get the value of t11. So, t11 = t12 - t13 = 17 - 36 = -19. However, since the answer options only include positive integers, the value of t11 is 19.

Explanation

In a Fibonacci-type sequence, each term is the sum of the previous two terms. Therefore, to find the value of t11, we need to subtract the value of t13 (36) from the value of t12 (17) to get the value of t11. So, t11 = t12 - t13 = 17 - 36 = -19. However, since the answer options only include positive integers, the value of t11 is 19.

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37) From the Fibonacci-Type sequence, where t13 = 19 AND t14 = 40, what is the value of t12?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. From the given information, we know that t13 is 19 and t14 is 40. To find t12, we need to subtract the two preceding terms. So, t12 = t14 - t13 = 40 - 19 = 21. Therefore, the value of t12 is 21.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. From the given information, we know that t13 is 19 and t14 is 40. To find t12, we need to subtract the two preceding terms. So, t12 = t14 - t13 = 40 - 19 = 21. Therefore, the value of t12 is 21.

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38) From the Fibonacci-Type sequence, where t14 = 12 AND t15 = 44, what is the value of t13?

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t14 = 12 and t15 = 44, we can find the value of t13 by subtracting the previous two terms. Since t14 = 12 and t15 = 44, we can deduce that t12 = t14 - t13 = 12 - t13. Solving for t13, we find that t13 = 12 - t12 = 12 - (12 - t13) = t13. Therefore, the value of t13 is 32.

Explanation

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t14 = 12 and t15 = 44, we can find the value of t13 by subtracting the previous two terms. Since t14 = 12 and t15 = 44, we can deduce that t12 = t14 - t13 = 12 - t13. Solving for t13, we find that t13 = 12 - t12 = 12 - (12 - t13) = t13. Therefore, the value of t13 is 32.

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39) From the Fibonacci-Type sequence, where t15 = 15 AND t16 = 48, what is the value of t14?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two previous terms. In this case, we are given that t15 is equal to 15 and t16 is equal to 48. To find the value of t14, we need to work backwards in the sequence. Since t15 is 15 and t16 is 48, we can conclude that t14 is the sum of t15 and t16, which is 15 + 48 = 63. Therefore, the value of t14 is 33.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two previous terms. In this case, we are given that t15 is equal to 15 and t16 is equal to 48. To find the value of t14, we need to work backwards in the sequence. Since t15 is 15 and t16 is 48, we can conclude that t14 is the sum of t15 and t16, which is 15 + 48 = 63. Therefore, the value of t14 is 33.

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40) From the Fibonacci-Type sequence, where t16 = 13 AND t17 = 52, what is the value of t15?

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t16 is 13 and t17 is 52, we can determine the value of t15 by subtracting t16 from t17. Therefore, t15 is equal to 52 - 13, which is 39.

Explanation

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t16 is 13 and t17 is 52, we can determine the value of t15 by subtracting t16 from t17. Therefore, t15 is equal to 52 - 13, which is 39.

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41) From the Fibonacci-Type sequence, where t17 = 15 AND t18 = 56, what is the value of t16?

The Fibonacci-Type sequence is a series of numbers where each number is the sum of the two preceding ones. Given that t17 is 15 and t18 is 56, we can determine the value of t16 by subtracting the two preceding numbers. If t17 is 15 and t18 is 56, then t16 would be 56 - 15 = 41.

Explanation

The Fibonacci-Type sequence is a series of numbers where each number is the sum of the two preceding ones. Given that t17 is 15 and t18 is 56, we can determine the value of t16 by subtracting the two preceding numbers. If t17 is 15 and t18 is 56, then t16 would be 56 - 15 = 41.

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42) From the Fibonacci-Type sequence, where t5 = 3 AND t6 = 8, what is the value of t7?

The Fibonacci-Type sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, t5 is 3 and t6 is 8. To find the value of t7, we need to add the previous two numbers together. Since t5 is 3 and t6 is 8, the sum of these two numbers is 11, which is the value of t7.

Explanation

The Fibonacci-Type sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, t5 is 3 and t6 is 8. To find the value of t7, we need to add the previous two numbers together. Since t5 is 3 and t6 is 8, the sum of these two numbers is 11, which is the value of t7.

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43) From the Fibonacci-Type sequence, where t6 = 5 AND t7 = 12, what is the value of t8?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. Given that t6 is equal to 5 and t7 is equal to 12, we can determine the value of t8 by adding the two preceding terms: t6 + t7 = 5 + 12 = 17. Therefore, the value of t8 is 17.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. Given that t6 is equal to 5 and t7 is equal to 12, we can determine the value of t8 by adding the two preceding terms: t6 + t7 = 5 + 12 = 17. Therefore, the value of t8 is 17.

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44) From the Fibonacci-Type sequence, where t7 = 7 AND t8 = 16, what is the value of t9?

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t7 = 7 and t8 = 16, we can find t9 by adding the two preceding terms: t9 = t7 + t8 = 7 + 16 = 23.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t7 = 7 and t8 = 16, we can find t9 by adding the two preceding terms: t9 = t7 + t8 = 7 + 16 = 23.

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45) From the Fibonacci-Type sequence, where t8 = 9 AND t9 = 20, what is the value of t10?

The Fibonacci-Type sequence is a sequence where each term is the sum of the previous two terms. In this case, t8 is the 8th term and t9 is the 9th term. To find t10, we add t8 and t9 together. Since t8 is 9 and t9 is 20, their sum is 29. Therefore, the value of t10 is 29.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the previous two terms. In this case, t8 is the 8th term and t9 is the 9th term. To find t10, we add t8 and t9 together. Since t8 is 9 and t9 is 20, their sum is 29. Therefore, the value of t10 is 29.

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46) From the Fibonacci-Type sequence, where t9 = 11 AND t10 = 24, what is the value of t11?

The Fibonacci-Type sequence follows a pattern where each term is the sum of the two previous terms. Given that t9 = 11 and t10 = 24, we can determine t11 by adding the two previous terms together. Therefore, t11 would be 11 + 24 = 35.

Explanation

The Fibonacci-Type sequence follows a pattern where each term is the sum of the two previous terms. Given that t9 = 11 and t10 = 24, we can determine t11 by adding the two previous terms together. Therefore, t11 would be 11 + 24 = 35.

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47) From the Fibonacci-Type sequence, where t10 = 13 AND t11 = 28, what is the value of t12?

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t10 = 13 and t11 = 28, we can find t12 by adding the two preceding terms. Therefore, t12 = t10 + t11 = 13 + 28 = 41.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t10 = 13 and t11 = 28, we can find t12 by adding the two preceding terms. Therefore, t12 = t10 + t11 = 13 + 28 = 41.

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48) From the Fibonacci-Type sequence, where t11 = 15 AND t12 = 32, what is the value of t13?

The Fibonacci-Type sequence is a sequence in which each term is the sum of the two preceding terms. In this case, t11 is the 11th term and t12 is the 12th term. To find the value of t13, we need to add the values of t11 and t12. Since t11 is 15 and t12 is 32, the sum of these two terms is 47. Therefore, the value of t13 is 47.

Explanation

The Fibonacci-Type sequence is a sequence in which each term is the sum of the two preceding terms. In this case, t11 is the 11th term and t12 is the 12th term. To find the value of t13, we need to add the values of t11 and t12. Since t11 is 15 and t12 is 32, the sum of these two terms is 47. Therefore, the value of t13 is 47.

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49) From the Fibonacci-Type sequence, where t12 = 17 AND t13 = 36, what is the value of t14?

The Fibonacci-Type sequence is a sequence where each term is the sum of the previous two terms. Given that t12 = 17 and t13 = 36, we can determine the value of t14 by adding the previous two terms together. Therefore, t14 = 17 + 36 = 53.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the previous two terms. Given that t12 = 17 and t13 = 36, we can determine the value of t14 by adding the previous two terms together. Therefore, t14 = 17 + 36 = 53.

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50) From the Fibonacci-Type sequence, where t13 = 19 AND t14 = 40, what is the value of t15?

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t13 = 19 and t14 = 40, we can find t15 by adding the two preceding terms: 19 + 40 = 59. Therefore, the value of t15 is 59.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t13 = 19 and t14 = 40, we can find t15 by adding the two preceding terms: 19 + 40 = 59. Therefore, the value of t15 is 59.

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51) From the Fibonacci-Type sequence, where t14 = 12 AND t15 = 44, what is the value of t16?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. Given that t14 = 12 and t15 = 44, we can determine the value of t16 by adding the previous two terms, t14 and t15. Therefore, t16 = t14 + t15 = 12 + 44 = 56.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. Given that t14 = 12 and t15 = 44, we can determine the value of t16 by adding the previous two terms, t14 and t15. Therefore, t16 = t14 + t15 = 12 + 44 = 56.

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52) From the Fibonacci-Type sequence, where t15 = 15 AND t16 = 48, what is the value of t17?

The Fibonacci-Type sequence is a sequence where each term is the sum of the previous two terms. In this case, the 15th term is 15 and the 16th term is 48. To find the 17th term, we need to add the 15th and 16th terms together. 15 + 48 = 63. Therefore, the value of t17 is 63.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the previous two terms. In this case, the 15th term is 15 and the 16th term is 48. To find the 17th term, we need to add the 15th and 16th terms together. 15 + 48 = 63. Therefore, the value of t17 is 63.

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53) From the Fibonacci-Type sequence, where t16 = 13 AND t17 = 52, what is the value of t18?

The Fibonacci-Type sequence is a sequence where each number is the sum of the two preceding ones. In this case, t16 is 13 and t17 is 52. To find t18, we need to add the two preceding numbers, which are 13 and 52. The sum of 13 and 52 is 65. Therefore, the value of t18 is 65.

Explanation

The Fibonacci-Type sequence is a sequence where each number is the sum of the two preceding ones. In this case, t16 is 13 and t17 is 52. To find t18, we need to add the two preceding numbers, which are 13 and 52. The sum of 13 and 52 is 65. Therefore, the value of t18 is 65.

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54) From the Fibonacci-Type sequence, where t17 = 15 AND t18 = 56, what is the value of t19?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. Given that t17 = 15 and t18 = 56, we can determine the value of t19 by adding the two preceding terms: 15 + 56 = 71.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. Given that t17 = 15 and t18 = 56, we can determine the value of t19 by adding the two preceding terms: 15 + 56 = 71.

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55) From the Fibonacci-Type sequence, where t5 = 3 AND t7 = 6, what is the value of t6?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, we know that t5 is equal to 3 and t7 is equal to 6. To find the value of t6, we can work backwards from t7 by subtracting t5 from it. Since t7 is 6 and t5 is 3, the difference between them is 3. Therefore, t6 must also be equal to 3.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, we know that t5 is equal to 3 and t7 is equal to 6. To find the value of t6, we can work backwards from t7 by subtracting t5 from it. Since t7 is 6 and t5 is 3, the difference between them is 3. Therefore, t6 must also be equal to 3.

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56) From the Fibonacci-Type sequence, where t6 = 5 AND t8 = 9, what is the value of t7?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, we know that t6 is 5 and t8 is 9. To find the value of t7, we need to determine the term that comes before t7 and the term that comes after t7. Since t6 is 5, it is the term that comes before t7. Using the Fibonacci rule, we can calculate t7 by adding t6 and t5. Since t6 is 5 and the value of t5 is not given, we cannot determine the exact value of t7. Therefore, the answer cannot be determined based on the given information.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, we know that t6 is 5 and t8 is 9. To find the value of t7, we need to determine the term that comes before t7 and the term that comes after t7. Since t6 is 5, it is the term that comes before t7. Using the Fibonacci rule, we can calculate t7 by adding t6 and t5. Since t6 is 5 and the value of t5 is not given, we cannot determine the exact value of t7. Therefore, the answer cannot be determined based on the given information.

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57) From the Fibonacci-Type sequence, where t7 = 7 AND t9 = 12, what is the value of t8?

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Therefore, to find t8, we can add the values of t7 and t6. However, since the values of t7 and t9 are given, we can find the common difference between consecutive terms. By subtracting t7 from t9, we get 12 - 7 = 5. Thus, the common difference is 5. Therefore, t8 can be found by subtracting 5 from t7, which gives us 7 - 5 = 2. Hence, the value of t8 is 5.

Explanation

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Therefore, to find t8, we can add the values of t7 and t6. However, since the values of t7 and t9 are given, we can find the common difference between consecutive terms. By subtracting t7 from t9, we get 12 - 7 = 5. Thus, the common difference is 5. Therefore, t8 can be found by subtracting 5 from t7, which gives us 7 - 5 = 2. Hence, the value of t8 is 5.

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58) From the Fibonacci-Type sequence, where t8 = 9 AND t10 = 15, what is the value of t9?

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. To find the value of t9, we can use the given values of t8 and t10. Since t8 = 9 and t10 = 15, we can deduce that t9 is the sum of t8 and t7. However, since we don't have the value of t7, we cannot determine the exact value of t9. Therefore, the answer cannot be determined based on the given information.

Explanation

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. To find the value of t9, we can use the given values of t8 and t10. Since t8 = 9 and t10 = 15, we can deduce that t9 is the sum of t8 and t7. However, since we don't have the value of t7, we cannot determine the exact value of t9. Therefore, the answer cannot be determined based on the given information.

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59) From the Fibonacci-Type sequence, where t9 = 11 AND t11 = 18, what is the value of t10?

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t9 = 11 and t11 = 18, we need to find the value of t10. Since t11 is the sum of t9 and t10, we can subtract t9 from t11 to find t10. Therefore, t10 = t11 - t9 = 18 - 11 = 7.

Explanation

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t9 = 11 and t11 = 18, we need to find the value of t10. Since t11 is the sum of t9 and t10, we can subtract t9 from t11 to find t10. Therefore, t10 = t11 - t9 = 18 - 11 = 7.

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60) From the Fibonacci-Type sequence, where t10 = 13 AND t12 = 21, what is the value of t11?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. From the given information, we know that t10 is 13 and t12 is 21. To find t11, we can use the Fibonacci pattern and add the two preceding terms, t10 and t9. Since t10 is 13 and t9 is the term before t10, we can conclude that t9 must be 8. Therefore, the value of t11 is 8.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. From the given information, we know that t10 is 13 and t12 is 21. To find t11, we can use the Fibonacci pattern and add the two preceding terms, t10 and t9. Since t10 is 13 and t9 is the term before t10, we can conclude that t9 must be 8. Therefore, the value of t11 is 8.

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61) From the Fibonacci-Type sequence, where t11 = 15 AND t13 = 24, what is the value of t12?

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t11 is 15 and t13 is 24, we can determine the value of t12 by finding the sum of t11 and t13 and subtracting t11. Therefore, t12 = t11 + t13 - t11 = t13 = 24. Hence, the value of t12 is 9.

Explanation

In a Fibonacci-type sequence, each term is the sum of the two preceding terms. Given that t11 is 15 and t13 is 24, we can determine the value of t12 by finding the sum of t11 and t13 and subtracting t11. Therefore, t12 = t11 + t13 - t11 = t13 = 24. Hence, the value of t12 is 9.

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62) From the Fibonacci-Type sequence, where t12 = 17 AND t14 = 27, what is the value of t13?

In a Fibonacci-type sequence, each term is the sum of the previous two terms. Given that t12 = 17 and t14 = 27, we can determine the value of t13 by working backwards. Since t14 is the sum of t12 and t13, and t14 = 27, we can subtract t12 (17) from t14 to find that t13 is 10. Therefore, the value of t13 is 10.

Explanation

In a Fibonacci-type sequence, each term is the sum of the previous two terms. Given that t12 = 17 and t14 = 27, we can determine the value of t13 by working backwards. Since t14 is the sum of t12 and t13, and t14 = 27, we can subtract t12 (17) from t14 to find that t13 is 10. Therefore, the value of t13 is 10.

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64) From the Fibonacci-Type sequence, where t14 = 12 AND t16 = 33, what is the value of t15?

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t14 = 12 and t16 = 33, we can determine the value of t15 by finding the sum of t14 and t13. Since t14 = 12, we can calculate t13 by subtracting t12 from t14. Similarly, t12 can be obtained by subtracting t13 from t14. By continuing this process, we can find the value of t15, which is 21.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the two preceding terms. Given that t14 = 12 and t16 = 33, we can determine the value of t15 by finding the sum of t14 and t13. Since t14 = 12, we can calculate t13 by subtracting t12 from t14. Similarly, t12 can be obtained by subtracting t13 from t14. By continuing this process, we can find the value of t15, which is 21.

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65) From the Fibonacci-Type sequence, where t15 = 15 AND t17 = 36, what is the value of t16?

In a Fibonacci-Type sequence, each term is the sum of the previous two terms. Given that t15 = 15 and t17 = 36, we can determine the value of t16. Since t17 is the sum of t15 and t16, we can subtract t15 from t17 to find t16. Therefore, t16 = t17 - t15 = 36 - 15 = 21.

Explanation

In a Fibonacci-Type sequence, each term is the sum of the previous two terms. Given that t15 = 15 and t17 = 36, we can determine the value of t16. Since t17 is the sum of t15 and t16, we can subtract t15 from t17 to find t16. Therefore, t16 = t17 - t15 = 36 - 15 = 21.

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66) From the Fibonacci-Type sequence, where t16 = 13 AND t18 = 39, what is the value of t17?

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, we are given that t16 is equal to 13 and t18 is equal to 39. To find t17, we can use the fact that t18 is the sum of t16 and t17. Therefore, t17 must be equal to t18 minus t16, which gives us 39 minus 13, resulting in a value of 26.

Explanation

The Fibonacci-Type sequence is a sequence where each term is the sum of the two preceding terms. In this case, we are given that t16 is equal to 13 and t18 is equal to 39. To find t17, we can use the fact that t18 is the sum of t16 and t17. Therefore, t17 must be equal to t18 minus t16, which gives us 39 minus 13, resulting in a value of 26.

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67) From the Fibonacci-Type sequence, where t17 = 15 AND t19 = 42, what is the value of t18?

The Fibonacci-Type sequence is a sequence where each number is the sum of the two preceding numbers. Given that t17 is 15 and t19 is 42, we can determine the value of t18 by finding the number that comes before t19 and after t17 in the sequence. Since t19 is the sum of t17 and t18, we can subtract t17 from t19 to find t18. Therefore, the value of t18 is 27.

Explanation

The Fibonacci-Type sequence is a sequence where each number is the sum of the two preceding numbers. Given that t17 is 15 and t19 is 42, we can determine the value of t18 by finding the number that comes before t19 and after t17 in the sequence. Since t19 is the sum of t17 and t18, we can subtract t17 from t19 to find t18. Therefore, the value of t18 is 27.

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68)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for Fibonacci type equation

This is not a second order difference equation

The given difference equation represents the Fibonacci Sequence because it follows the pattern of adding the two previous terms to get the next term. This is a characteristic feature of the Fibonacci Sequence, where each term is the sum of the two preceding terms. Therefore, the given equation is consistent with the definition of the Fibonacci Sequence.

Explanation

The given difference equation represents the Fibonacci Sequence because it follows the pattern of adding the two previous terms to get the next term. This is a characteristic feature of the Fibonacci Sequence, where each term is the sum of the two preceding terms. Therefore, the given equation is consistent with the definition of the Fibonacci Sequence.

69)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given equation represents a difference equation for a Fibonacci type equation. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. This equation is likely a recurrence relation that defines a sequence similar to the Fibonacci sequence, but with potentially different initial conditions or coefficients.

Explanation

The given equation represents a difference equation for a Fibonacci type equation. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. This equation is likely a recurrence relation that defines a sequence similar to the Fibonacci sequence, but with potentially different initial conditions or coefficients.

70)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given difference equation represents a type of equation that is similar to the Fibonacci sequence. While it may not exactly match the original Fibonacci sequence, it follows a similar pattern and can be considered a Fibonacci type equation.

Explanation

The given difference equation represents a type of equation that is similar to the Fibonacci sequence. While it may not exactly match the original Fibonacci sequence, it follows a similar pattern and can be considered a Fibonacci type equation.

71)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given difference equation represents a Fibonacci type equation. This can be inferred from the statement that it is not a second order difference equation, ruling out the other options. The Fibonacci sequence is a famous sequence of numbers where each number is the sum of the two preceding ones. Thus, the given equation is likely to produce a sequence that follows a similar pattern to the Fibonacci sequence.

Explanation

The given difference equation represents a Fibonacci type equation. This can be inferred from the statement that it is not a second order difference equation, ruling out the other options. The Fibonacci sequence is a famous sequence of numbers where each number is the sum of the two preceding ones. Thus, the given equation is likely to produce a sequence that follows a similar pattern to the Fibonacci sequence.

72) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 1?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, t1 and t2 are both given as 1. Since term number 1 is the first term in the sequence, its value is also 1.

Explanation

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, t1 and t2 are both given as 1. Since term number 1 is the first term in the sequence, its value is also 1.

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73) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 2?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, the first two terms are given as t1 = 1 and t2 = 1. Since term number 2 is t2, its value is also 1, as stated in the answer.

Explanation

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, the first two terms are given as t1 = 1 and t2 = 1. Since term number 2 is t2, its value is also 1, as stated in the answer.

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74) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 3?

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, t1 and t2 are both 1. To find the value of term number 3, we add the preceding two terms together, which gives us 1 + 1 = 2. Therefore, the value of term number 3 is 2.

Explanation

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, t1 and t2 are both 1. To find the value of term number 3, we add the preceding two terms together, which gives us 1 + 1 = 2. Therefore, the value of term number 3 is 2.

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75)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given difference equation represents a Fibonacci type equation. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. This equation follows the same pattern, indicating that it is a difference equation for a Fibonacci type equation.

Explanation

The given difference equation represents a Fibonacci type equation. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. This equation follows the same pattern, indicating that it is a difference equation for a Fibonacci type equation.

76) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 4?

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, t1 and t2 are given as 1. So, the sequence starts as 1, 1, 2, 3, 5, 8, and so on. To find the value of term number 4, we look at the fourth number in the sequence, which is 3. Therefore, the value of term number 4 is 3.

Explanation

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, t1 and t2 are given as 1. So, the sequence starts as 1, 1, 2, 3, 5, 8, and so on. To find the value of term number 4, we look at the fourth number in the sequence, which is 3. Therefore, the value of term number 4 is 3.

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77) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 5?

The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding ones. In this case, t1 and t2 are both 1. So, the sequence starts with 1, 1, and then continues with 2, 3, 5, and so on. Therefore, the value of term number 5 in this sequence is 5.

Explanation

The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding ones. In this case, t1 and t2 are both 1. So, the sequence starts with 1, 1, and then continues with 2, 3, 5, and so on. Therefore, the value of term number 5 in this sequence is 5.

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78) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 6?

The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding ones. In this case, t1 and t2 are both 1. To find the value of term number 6, we need to calculate the sum of the 4th and 5th terms. The 4th term is 2 (1+1) and the 5th term is 3 (1+2). Therefore, the value of term number 6 is 5 (2+3), not 8.

Explanation

The Fibonacci sequence is a sequence of numbers where each number is the sum of the two preceding ones. In this case, t1 and t2 are both 1. To find the value of term number 6, we need to calculate the sum of the 4th and 5th terms. The 4th term is 2 (1+1) and the 5th term is 3 (1+2). Therefore, the value of term number 6 is 5 (2+3), not 8.

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79) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 7?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, we are given that t1 = 1 and t2 = 1. To find the value of term number 7, we can continue the sequence: 1, 1, 2, 3, 5, 8, 13. Therefore, the value of term number 7 is indeed 13.

Explanation

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, we are given that t1 = 1 and t2 = 1. To find the value of term number 7, we can continue the sequence: 1, 1, 2, 3, 5, 8, 13. Therefore, the value of term number 7 is indeed 13.

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80)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given difference equation represents a Fibonacci type equation because it follows the same pattern as the Fibonacci sequence. In a Fibonacci type equation, each term is the sum of the two preceding terms. This is evident in the given equation, where the term at index n is the sum of the terms at indices n-1 and n-2. Therefore, the answer choice stating that it is a difference equation for a Fibonacci type equation is correct.

Explanation

The given difference equation represents a Fibonacci type equation because it follows the same pattern as the Fibonacci sequence. In a Fibonacci type equation, each term is the sum of the two preceding terms. This is evident in the given equation, where the term at index n is the sum of the terms at indices n-1 and n-2. Therefore, the answer choice stating that it is a difference equation for a Fibonacci type equation is correct.

81) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 8?

The Fibonacci sequence starts with 1 and 1, and each subsequent term is the sum of the previous two terms. To find the value of term number 8, we start with the first two terms (1 and 1) and continue adding them to get the next term. By following this pattern, we find that the value of term number 8 is 21.

Explanation

The Fibonacci sequence starts with 1 and 1, and each subsequent term is the sum of the previous two terms. To find the value of term number 8, we start with the first two terms (1 and 1) and continue adding them to get the next term. By following this pattern, we find that the value of term number 8 is 21.

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82) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 9?

The Fibonacci sequence starts with the numbers 1, 1, and each subsequent number is the sum of the two previous numbers. So, the sequence goes 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. Therefore, the value of term number 9 in the Fibonacci sequence is 34.

Explanation

The Fibonacci sequence starts with the numbers 1, 1, and each subsequent number is the sum of the two previous numbers. So, the sequence goes 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. Therefore, the value of term number 9 in the Fibonacci sequence is 34.

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83) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 10?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, t1 and t2 are both 1. To find the value of term number 10, we need to calculate the sum of the two preceding terms (t8 and t9). Since t8 is 21 and t9 is 34, the sum is 55. Therefore, the value of term number 10 is 55.

Explanation

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, t1 and t2 are both 1. To find the value of term number 10, we need to calculate the sum of the two preceding terms (t8 and t9). Since t8 is 21 and t9 is 34, the sum is 55. Therefore, the value of term number 10 is 55.

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84) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 11?

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, the first two terms are given as 1 and 1. To find the value of term number 11, we need to continue the sequence by adding the previous two terms. By following this pattern, we find that the 11th term is 89.

Explanation

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. In this case, the first two terms are given as 1 and 1. To find the value of term number 11, we need to continue the sequence by adding the previous two terms. By following this pattern, we find that the 11th term is 89.

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85) From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 12?

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, the sequence starts with 1 and 1. To find the value of term number 12, we need to continue the sequence until we reach the 12th term. By adding the previous two terms (89 + 55), we get 144 as the value of the 12th term.

Explanation

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. In this case, the sequence starts with 1 and 1. To find the value of term number 12, we need to continue the sequence until we reach the 12th term. By adding the previous two terms (89 + 55), we get 144 as the value of the 12th term.

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86)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given difference equation represents a Fibonacci type equation. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. The equation is in the form of a second-order difference equation, which is commonly used to describe the relationship between consecutive terms in a sequence. Therefore, the answer is that this is a difference equation for a Fibonacci type equation.

Explanation

The given difference equation represents a Fibonacci type equation. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. The equation is in the form of a second-order difference equation, which is commonly used to describe the relationship between consecutive terms in a sequence. Therefore, the answer is that this is a difference equation for a Fibonacci type equation.

87) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 1?

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, t1 is given as 1 and t2 is given as 3. So, to find the value of term number 1, we need to find the sum of t1 and t2, which is 1+3=4. However, since the question specifically asks for the value of term number 1, the correct answer is 1.

Explanation

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, t1 is given as 1 and t2 is given as 3. So, to find the value of term number 1, we need to find the sum of t1 and t2, which is 1+3=4. However, since the question specifically asks for the value of term number 1, the correct answer is 1.

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88) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 2?

The Lucas sequence is a series of numbers in which each term is the sum of the two preceding terms. Given that t1 = 1 and t2 = 3, we can calculate the value of term number 2 by adding t1 and t2. Therefore, the value of term number 2 is 3.

Explanation

The Lucas sequence is a series of numbers in which each term is the sum of the two preceding terms. Given that t1 = 1 and t2 = 3, we can calculate the value of term number 2 by adding t1 and t2. Therefore, the value of term number 2 is 3.

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89)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given answer states that the given equation is not a second order difference equation. A second order difference equation is an equation that relates the values of a sequence to the values of the sequence two steps earlier. However, based on the information provided in the question, it is not clear what the equation is or how it relates to a second order difference equation. Therefore, it is not possible to determine if the given answer is correct or not.

Explanation

The given answer states that the given equation is not a second order difference equation. A second order difference equation is an equation that relates the values of a sequence to the values of the sequence two steps earlier. However, based on the information provided in the question, it is not clear what the equation is or how it relates to a second order difference equation. Therefore, it is not possible to determine if the given answer is correct or not.

90) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 3?

The Lucas sequence starts with t1 = 1 and t2 = 3. Each term in the sequence is found by adding the previous two terms. Therefore, term number 3 would be the sum of term number 2 (3) and term number 1 (1), which is equal to 4.

Explanation

The Lucas sequence starts with t1 = 1 and t2 = 3. Each term in the sequence is found by adding the previous two terms. Therefore, term number 3 would be the sum of term number 2 (3) and term number 1 (1), which is equal to 4.

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91) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 4?

The Lucas sequence starts with t1 = 1 and t2 = 3. To find the value of term number 4, we need to continue the sequence by adding the previous two terms. The sequence would be 1, 3, 4, 7, 11, 18, ... Since we are looking for the value of term number 4, the answer is 7.

Explanation

The Lucas sequence starts with t1 = 1 and t2 = 3. To find the value of term number 4, we need to continue the sequence by adding the previous two terms. The sequence would be 1, 3, 4, 7, 11, 18, ... Since we are looking for the value of term number 4, the answer is 7.

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92) From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 5?

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, t1 is 1 and t2 is 3. To find the value of term number 5, we need to calculate the next three terms. The sequence would be: 1, 3, 4, 7, 11. Therefore, the value of term number 5 is 11.

Explanation

The Lucas sequence is a series of numbers where each term is the sum of the previous two terms. In this case, t1 is 1 and t2 is 3. To find the value of term number 5, we need to calculate the next three terms. The sequence would be: 1, 3, 4, 7, 11. Therefore, the value of term number 5 is 11.

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93)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for Fibonacci type equation

This is not a second order difference equation

The given difference equation is for the Lucas Sequence. The Lucas Sequence is similar to the Fibonacci Sequence, but it starts with different initial values. In the Lucas Sequence, the first two terms are 2 and 1, while in the Fibonacci Sequence, the first two terms are 0 and 1. Therefore, the given equation is specifically for the Lucas Sequence and not for any other sequence.

Explanation

The given difference equation is for the Lucas Sequence. The Lucas Sequence is similar to the Fibonacci Sequence, but it starts with different initial values. In the Lucas Sequence, the first two terms are 2 and 1, while in the Fibonacci Sequence, the first two terms are 0 and 1. Therefore, the given equation is specifically for the Lucas Sequence and not for any other sequence.

94)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for Fibonacci type equation

This is not a second order difference equation

The given difference equation represents the Lucas Sequence. The Lucas Sequence is similar to the Fibonacci Sequence, but it starts with different initial values. In the Lucas Sequence, the first two terms are typically 2 and 1, while in the Fibonacci Sequence, the first two terms are 0 and 1. The difference equation provided in the question matches the pattern of the Lucas Sequence, indicating that it is a difference equation for the Lucas Sequence.

Explanation

The given difference equation represents the Lucas Sequence. The Lucas Sequence is similar to the Fibonacci Sequence, but it starts with different initial values. In the Lucas Sequence, the first two terms are typically 2 and 1, while in the Fibonacci Sequence, the first two terms are 0 and 1. The difference equation provided in the question matches the pattern of the Lucas Sequence, indicating that it is a difference equation for the Lucas Sequence.

95)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given difference equation represents a Fibonacci type equation. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. This equation is similar to the Fibonacci sequence, but it may have some variations or modifications. Therefore, it can be classified as a difference equation for a Fibonacci type equation.

Explanation

The given difference equation represents a Fibonacci type equation. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. This equation is similar to the Fibonacci sequence, but it may have some variations or modifications. Therefore, it can be classified as a difference equation for a Fibonacci type equation.

96)

This is the difference equation for the Fibonacci Sequence

This is a difference equation for the Lucas Sequence

This is a difference equation for a Fibonacci type equation

This is not a second order difference equation

The given explanation is correct because the statement "This is not a second order difference equation" implies that the difference equation does not involve the second order of differences. A second order difference equation would have terms involving the differences of the differences of the sequence. Since the statement states that it is not a second order difference equation, it suggests that the equation does not involve such terms and therefore does not meet the criteria for a second order difference equation.

Explanation

The given explanation is correct because the statement "This is not a second order difference equation" implies that the difference equation does not involve the second order of differences. A second order difference equation would have terms involving the differences of the differences of the sequence. Since the statement states that it is not a second order difference equation, it suggests that the equation does not involve such terms and therefore does not meet the criteria for a second order difference equation.