9054 Any Solution From A & D

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Anthony Nunan
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Using the first term (a) and the common difference (d), find the solution for the following problems.

• 1.

When a = 30,    and d = 100 The rule for the Arithmetic Sequence is

Explanation
The given answer, -70+100n, represents the formula for finding the nth term of an arithmetic sequence. In this case, the common difference (d) is 100, meaning that each term in the sequence increases by 100. The first term (a) is 30. By substituting these values into the formula, we can find any term in the sequence by replacing n with the desired position of the term.

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• 2.

• 3.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 32 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 4.

Above are the values for the first term and common difference for an Arithmetic Series. A series is the sum of a sequence. Also provided is a value for 'n', the total number of terms in the series. Find the value for the series.

Explanation
a is the first term, d is the common difference. Use the Series rule OR an App to calculate the term. Higher term values are on page 1.3 in the table. Make sure you use the 'series' column, not the 'sequence' column.

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• 5.

• 6.

When a =  1,    and d = 4 The rule for the Arithmetic Sequence is

Explanation
The given answer, -3+4n, represents the formula for finding the nth term of an arithmetic sequence. In this formula, -3 is the initial term (a) and 4 is the common difference (d). By substituting the values of a=1 and d=4, we can find any term in the sequence by plugging in the value of n.

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• 7.

• 8.

When a = 38,    and d = 10 The rule for the Arithmetic Sequence is

Explanation
The rule for the Arithmetic Sequence is given by the formula a + dn, where a is the first term, d is the common difference, and n is the term number. In this case, a = 28 and d = 10. So, the correct answer is 28 + 10n, which represents the nth term of the arithmetic sequence when a = 28 and d = 10.

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• 9.

When a = 6,    and d = 10 The rule for the Arithmetic Sequence is

Explanation
The given answer, -4+10n, represents the formula for finding the nth term of an arithmetic sequence when the first term (a) is 6 and the common difference (d) is 10. In this case, the formula simplifies to -4+10n, where n represents the position of the term in the sequence.

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• 10.

• 11.

• 12.

• 13.

When a = 18,    and d = -9 The rule for the Arithmetic Sequence is

Explanation
The given answer, 27-9n, is the rule for the arithmetic sequence when a = 18 and d = -9. In an arithmetic sequence, the first term is represented by 'a' and the common difference between each term is represented by 'd'. By substituting the given values into the rule, we get 27-9n as the expression to find the nth term of the sequence.

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• 14.

• 15.

• 16.

• 17.

• 18.

• 19.

When a = -24,    and d = -5 The rule for the Arithmetic Sequence is

Explanation
The given expression represents the general term of an arithmetic sequence. In an arithmetic sequence, each term is obtained by adding a constant difference (d) to the previous term. In this case, the constant difference is -5. Therefore, the general term can be written as -19 - 5n, where n represents the position of the term in the sequence.

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• 20.

• 21.

• 22.

• 23.

When a = -14,    and d = 9 The rule for the Arithmetic Sequence is

Explanation
The given answer, -23+9n, represents the formula for finding the nth term of an arithmetic sequence. In this case, the first term (a) is -14 and the common difference (d) is 9. By substituting these values into the formula, we get -23+9n. This means that each term in the sequence can be found by multiplying the position of the term (n) by 9 and then subtracting 23.

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• 24.

When a = -7,    and d = 7 The rule for the Arithmetic Sequence is

Explanation
The given answer, -14+7n, represents the rule for the arithmetic sequence when a = -7 and d = 7. In an arithmetic sequence, each term is found by adding a constant difference, d, to the previous term. In this case, the first term is -7 and the common difference is 7. By substituting these values into the formula, we get -14+7n, where n represents the position of the term in the sequence. This formula allows us to find any term in the sequence by plugging in the corresponding value of n.

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• 25.

When a = -31,    and d = 9 The rule for the Arithmetic Sequence is

Explanation
The given rule for the arithmetic sequence is -40+9n. This means that the nth term of the sequence can be found by multiplying the common difference, which is 9, by the position of the term in the sequence, n, and then subtracting 40. In this case, when a = -31, we can substitute this value into the rule to find the term. So, the term would be -40 + 9n = -40 + 9(-31) = -40 - 279 = -319.

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• 26.

When a = -11,    and d = 200 The rule for the Arithmetic Sequence is

Explanation
The given expression represents the formula for finding the nth term of an arithmetic sequence. In this case, the first term (a) is -11 and the common difference (d) is 200. By substituting these values into the formula, we can find any term in the sequence by replacing the "n" with the desired term number. For example, to find the 5th term, we would replace "n" with 5 and simplify the expression to get -211+200(5) = -211+1000 = 789.

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• 27.

When a = -4,    and d = 7 The rule for the Arithmetic Sequence is

Explanation
The given answer, -11+7n, represents the formula for finding the nth term of an arithmetic sequence. In this case, the first term (a) is -4 and the common difference (d) is 7. By substituting these values into the formula, we can determine any term in the sequence by replacing n with the desired term number. For example, if we want to find the 5th term, we would substitute n=5 into the formula: -11+7(5) = 24. Therefore, the 5th term of the sequence is 24.

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• 28.

When a = -29,    and d = 5 The rule for the Arithmetic Sequence is

Explanation
The given rule for the arithmetic sequence is -34+5n, where n represents the position of the term in the sequence. This means that each term in the sequence can be found by substituting the corresponding value of n into the equation. In this case, when a = -29 and d = 5, we can find the term by substituting n = 1 into the equation: -34 + 5(1) = -29. Therefore, the correct answer is -29.

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• 29.

When a = -21,    and d = 2 The rule for the Arithmetic Sequence is

Explanation
The given rule for the arithmetic sequence is -23+2n. This means that to find any term in the sequence, we need to substitute the value of n (the position of the term) into the equation. In this case, since a = -21, we can substitute -21 into the equation and solve for n. Thus, the correct answer is -23+2n.

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• 30.

When a = -33,    and d = 10The rule for the Arithmetic Sequence is

Explanation
The given answer, -43+10n, represents the rule for the arithmetic sequence when a = -33 and d = 10. In an arithmetic sequence, each term is found by adding a constant difference (d) to the previous term. In this case, the first term (a) is -33 and the common difference (d) is 10. By substituting these values into the given rule, we get -43+10n, which represents the nth term of the arithmetic sequence.

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• 31.

When a = -14,    and d = 9 The rule for the Arithmetic Sequence is

Explanation
The given arithmetic sequence is represented by the formula -23 + 9n, where n represents the position of each term in the sequence. By substituting the values of a = -14 and d = 9 into the formula, we can find the correct answer.

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• 32.

When a = -36,    and d = 20 The rule for the Arithmetic Sequence is

Explanation
The given answer, -56+20n, represents the rule for the arithmetic sequence when a = -36 and d = 20. In an arithmetic sequence, each term is found by adding a constant difference, d, to the previous term. In this case, the first term is -36 and the common difference is 20. By substituting these values into the formula, we get -56+20n, where n represents the position of a term in the sequence. This formula will give us the correct term for any position in the sequence.

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• 33.

When a = -16,    and d = 20 The rule for the Arithmetic Sequence is

Explanation
The given rule for the arithmetic sequence is -36+20n, where n represents the position of the term in the sequence. This means that each term in the sequence can be found by substituting the value of n into the equation. In this case, when a = -16 and d = 20, we can substitute these values into the equation to find the answer. Therefore, the answer is -36+20n.

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• 34.

When a = -26,    and d = 20 The rule for the Arithmetic Sequence is

Explanation
The given answer, -46+20n, represents the formula for finding the nth term of an arithmetic sequence. In this case, the first term of the sequence is -46 and the common difference between each term is 20. By substituting the value of n, the position of the term in the sequence, we can calculate the corresponding term.

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• 35.

• 36.

When a = 28,    and d = 30 The rule for the Arithmetic Sequence is

Explanation
The given answer, -2+30n, represents the formula for finding the nth term of an arithmetic sequence. In this case, the common difference (d) is 30, meaning that each term in the sequence is obtained by adding 30 to the previous term. The first term (a) is 28. By substituting these values into the formula, we can find any term in the sequence by replacing "n" with the desired term number.

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• 37.

When a = 3,    and d = 200 The rule for the Arithmetic Sequence is

Explanation
The given answer is an expression that represents the nth term of an arithmetic sequence. In this case, the common difference (d) is 200 and the first term (a) is 3. The expression -197+200n represents the formula for finding the nth term of the sequence. By substituting the values of a and d into the formula, we can find any term in the sequence by plugging in the value of n.

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• 38.

When a = 31,    and d = 200 The rule for the Arithmetic Sequence is

Explanation
The given answer, -169+200n, represents the formula for finding the nth term of an arithmetic sequence when the first term (a) is 31 and the common difference (d) is 200. In this formula, -169 represents the difference between the first term and the constant term, and 200n represents the product of the common difference and the position of the term in the sequence. By substituting different values of n into the formula, we can find the corresponding terms of the arithmetic sequence.

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• 39.

When a = 26,    and d = 5 The rule for the Arithmetic Sequence is

Explanation
The given answer, 21+5n, represents the rule for the arithmetic sequence when a = 26 and d = 5. In an arithmetic sequence, each term is found by adding a constant difference, d, to the previous term. In this case, the first term, a, is 26, and the common difference, d, is 5. Therefore, the rule for finding the nth term in this arithmetic sequence is 21+5n, where n represents the position of the term in the sequence.

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• 40.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 34 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 41.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 35 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 42.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 40 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 43.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 31 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 44.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 34 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 45.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 22 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 46.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 23 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 47.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 21 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 48.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 38 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 49.

Above are the values for first term and common difference for an Arithmetic Sequence. What is the value of term 24 of this sequence?

Explanation
a is the first term, d is the common difference. Use the rule OR the App to calculate the term. Larger values are on page 1.3 in the table.

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• 50.

Above are the values for the first term and common difference for an Arithmetic Series. A series is the sum of a sequence. Also provided is a value for 'n', the total number of terms in the series. Find the value for the series.

Explanation
a is the first term, d is the common difference. Use the Series rule OR an App to calculate the term. Higher term values are on page 1.3 in the table. Make sure you use the 'series' column, not the 'sequence' column.

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• Current Version
• Mar 21, 2023
Quiz Edited by
ProProfs Editorial Team
• May 11, 2015
Quiz Created by
Anthony Nunan