Question

Write an recursive formula for An, the nth term of the sequence
5, -2, -9,

Answer 1

Given:

The given sequence is:

`5,-2,-9,...`

To find:

The recursive formula for
`a_n`, the nth term of the sequence.

Solution:

We have,

`5,-2,-9,...`

Here, the first term is 5.

`-2-5=-7`

`-9-(-2)=-9+2`

`-9-(-2)=-7`

The common difference is -7.

The recursive formula for the nth term of the sequence is

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

Where,
`d` is the common difference.

Putting
`d=-7` in the above formula, we get

`a_n=a_(n-1)+(-7)`

`a_n=a_(n-1)-7`

Therefore, the recursive formula for the nth term of the sequence is
`a_n=a_(n-1)-7`.