1.
Correct Answer
A. This is the difference equation for 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.
2.
Correct Answer
B. This 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.
3.
Correct Answer
B. This is a difference equation for the Lucas 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.
4.
Correct Answer
C. This is a difference equation for a Fibonacci type equation
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.
5.
Correct Answer
C. This is a difference equation for 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.
6.
Correct Answer
C. This is a difference equation for a Fibonacci type equation
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.
7.
Correct Answer
C. 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. 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.
8.
Correct Answer
C. 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. This equation follows the same pattern, indicating that it is a difference equation for a Fibonacci type equation.
9.
Correct Answer
C. This is a difference equation for a Fibonacci type equation
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.
10.
Correct Answer
C. 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.
11.
Correct Answer
D. This is not a second order difference equation
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.
12.
Correct Answer
D. This is not a second order difference equation
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.
13.
Correct Answer
D. This 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.
14.
Correct Answer
D. This 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.
15.
Correct Answer
D. This 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 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.
16.
Correct Answer
D. This is not 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.
17.
Correct Answer
D. This 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.
18.
Correct Answer
D. This is not 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.
19.
Correct Answer
D. This 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 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.
20.
Correct Answer
D. This is not 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.
Correct Answer
D. This is not a second order difference equation
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.
22.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 1?
Correct Answer
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.
23.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 2?
Correct Answer
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, 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.
24.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 3?
Correct Answer
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.
25.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 4?
Correct Answer
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.
26.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 5?
Correct Answer
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.
27.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 6?
Correct Answer
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.
28.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 7?
Correct Answer
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.
29.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 8?
Correct Answer
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.
30.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 9?
Correct Answer
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.
31.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 10?
Correct Answer
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.
32.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 11?
Correct Answer
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.
33.
From the Fibonacci sequence, where t1 = 1 and t2 = 1, what is the value of term number 12?
Correct Answer
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 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.
34.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 1?
Correct Answer
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.
35.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 2?
Correct Answer
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.
36.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 3?
Correct Answer
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.
37.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 4?
Correct Answer
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.
38.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 5?
Correct Answer
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.
39.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 6?
Correct Answer
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.
40.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 7?
Correct Answer
29
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).
41.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 8?
Correct Answer
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.
42.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 9?
Correct Answer
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.
43.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 10?
Correct Answer
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.
44.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 11?
Correct Answer
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.
45.
From the Lucas sequence, where t1 = 1 and t2 = 3, what is the value of term number 12?
Correct Answer
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.
46.
From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 1?
Correct Answer
2
Explanation
The value of term number 1 in the Fibonacci-Type sequence is 2.
47.
From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 2?
Correct Answer
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.
48.
From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 3?
Correct Answer
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.
49.
From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 4?
Correct Answer
8
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.
50.
From the Fibonacci-Type sequence, where t1 = 2 and t2 = 3, what is the value of term number 5?
Correct Answer
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.