Question

The recursive rule for a sequence is a^n=a^(n-1)+7,where a^1=-15. What is the explicit rule for this sequence?

Answer 1

ANSWER

$a_n=7n - 22$

EXPLANATION

The recursive rule for the sequence is

$a_n=a_{n-1}+7$

In general the recursive rule is written as:

$a_n=a_{n-1}+d$

This implies that, d=7

The first term of the sequence is

$a_1= - 15$

The explicit rule is given by:

$a_n=a_1 + d(n - 1)$

We substitute to get;

$a_n= - 15 + 7(n - 1)$

$a_n= - 15 + 7n - 7$

$a_n=7n - 22$