Exercise 81 Page 577

An explicit formula describes the

n^{th}

term of a sequence using the number

n .

A recursive formula relates consecutive terms. Consider the given formula.

a_{n} = a_{n - 1} + 13, where a_{1} = - 121

This formula relates a term $a_{n}$ with the previous one, $a_{n - 1} .$ Therefore, it is a recursive formula. Note that we are already given the first term, $a_{1} = - 121 .$ Let's find the next four terms.

$n$	$a_{n - 1}$	$a_{n - 1} + 13$	$a_{n} = a_{n - 1} + 13$
$2$	$a_{1} = - 121$	$- 121 + 13$	$a_{2} = - 108$
$3$	$a_{2} = - 108$	$- 108 + 13$	$a_{3} = - 95$
$4$	$a_{3} = 21$	$- 95 + 13$	$a_{4} = - 82$
$5$	$a_{4} = - 82$	$- 82 + 13$	$a_{5} = - 69$

We have found the first five terms of the given sequence.

a_{1} = - 121, a_{2} = - 108, a_{3} = - 95, a_{4} = - 82, and a_{5} = - 69