An arithmetic sequence is defined recursively by [math]a_n = a_{n - 1} + 5[/math], with [math]a_1[/math] = 29. Find the first 5 terms of the sequence, write an explicit formula to represent the sequence, and find the 15th term.
[list=1] [*]Use the recursive formula to find the first five terms of the sequence. [*]The first term is [math]a_1[/math] = 29 and the common difference is [math]d[/math] = 5, so the explicit formula is [math]a_n = 29 + (n - 1)5[/math]. [*]Simplify. [*]Substitute 15 in for [math]n[/math] to find the 15th term in the sequence. [/list]