Question

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For which scenario would it be best to use the recursive arithmetic formula?

You know the first term of the sequence and the common difference. You are looking for the twenty-fifth term in the sequence.

The first term of the sequence is 25. The common difference is 6. You are looking for the eighty-first term in the sequence.

You have the arithmetic sequence
. You need to find the fourth term in the sequence.

You have the arithmetic sequence
. You need to find the sixty-third term in the sequence.

Answer 1

Use the recursive formula when you only need a few next terms (small n) or you only have the previous term. So the best choice is:

- "You have the arithmetic sequence … You need to find the fourth term in the sequence."

Reason: the recursive rule a_n = a_{n-1} + d is easy to apply repeatedly for small n (find a2, a3, a4). For large n (25th, 63rd, 81st) the explicit formula a_n = a_1 + (n−1)d is more efficient.