Example 3

An arithmetic sequence is defined recursively by , with = 29. Find the first 5 terms of the sequence, write an explicit formula to represent the sequence, and find the 15th term.

1. Use the recursive formula to find the first five terms of the sequence.
2. The first term is = 29 and the common difference is = 5, so the explicit formula is .
3. Simplify.
4. Substitute 15 in for to find the 15th term in the sequence.

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