Question

Find the explicit formula for a 1 =-4,a n =a n-1 +9,n>=2

Answer 1

Given:

`a_1=-4` and
`a_n=a_(n-1)+9` where
`n\geq 2`.

To find:

The explicit formula for the given recursive formula.

Solution:

We know that recursive formula of an AP is:

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

Where, d is the common difference.

We have,

`a_n=a_(n-1)+9`

Here, d=9.

The first term of the AP is
`a_1=-4`.

The explicit formula for an AP is:

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

Substituting
`a_1=-4` and
`d=9`, we get

`a_n=-4+(n-1)9`

`a_n=-4+9n-9`

`a_n=-13+9n`

Therefore, the required explicit formula for the given sequence is
`a_n=-13+9n`.