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

`a_n=7n - 22`

Step-by-step 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`