Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

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How do you find the common difference in an arithmetic sequence?

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The common difference (d) can be found by subtracting any term from the subsequent term: d = a_{n+1} - a_n.

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What is the explicit formula for the nth term of an arithmetic sequence?

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The explicit formula is given by: a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

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What is the recursive formula for an arithmetic sequence?

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The recursive formula is given by: a_n = a_{n-1} + d, where d is the common difference.

Front

Given the explicit rule a_n = 2n + 5, what are the first four terms of the sequence?

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The first four terms are 7, 9, 11, 13.

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How do you identify the common difference in a sequence?

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To identify the common difference, subtract the first term from the second term. For example, in the sequence 97, 86, 75, 64, the common difference is -11.

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What is the recursive rule for the sequence 17, 10, 3, -4, -11?

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The recursive rule is a_n = a_{n-1} - 7.

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What is the recursive rule for the sequence -5, -1, 3, 7, 11?

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The recursive rule is a_n = a_{n-1} + 4.

Front

How do you find the nth term of an arithmetic sequence?

Back

To find the nth term, use the formula: a_n = a_1 + (n - 1)d.

Front

If a_1 = 5 and d = 0.5, what is the 25th term of the sequence?

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The 25th term is 17.