Question

A recursive rule for an arithmetic sequence is a1=−3;an=an−1+7a1=−3;an=an−1+7.

What is an explicit rule for this sequence?

Answer 1

To summarize the process of writing an explicit formula for an arithmetic sequence:

1. Determine if the sequence is arithmetic (Do you add, or subtract, the same amount from one term to the next?)

2. Find the common difference. (The number you add or subtract.)

3. Create an explicit formula using the pattern of the first term added to the product of the common difference and one less than the term number.

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