Question

Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form.

Answer 1

`a_n = -11-14n`

Explanation:

Given

`a_1 = -25`

`a_n = a_(n-1)-14`

Required

The explicit formula

First, calculate
`a_2`

Set n=2; So:

`a_2 = a_(2-1)-14`

`a_2 = a_(1)-14`

Substitute -25 for
`a_1`

`a_2 = -25-14`

`a_2 = -39`

Calculate the common difference (d)

`d = a_2 - a_1`

`d = -39 --25`

`d = -14`

So, the nth term is:

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

`a_n = -25+ (n - 1)*-14`

Open bracket

`a_n = -25-14n + 14`

Collect like terms

`a_n = 14-25-14n`

`a_n = -11-14n`