Question

Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?

5,–1, –7, –13, –19

Answer 1

C

Explanation:

Answer 2

`f(n)=f(n-1)-6`, where
`f(1)=5` and
`n\:>\:1`

Explanation:

The terms of the sequence are:

`5,-1,-7,-13,-19`

The first term of this sequence is
`f(1)=5`.

There is a constant difference among the terms.

This constant difference can determined by subtracting a previous term from a subsequent term.

`d=-1-5=-6`

The general term of this arithmetic sequence is given recursively by
`f(n)=f(n-1)+d`

We substitute the necessary values to obtain:

`f(n)=f(n-1)+-6`

Or

`f(n)=f(n-1)-6`, where
`f(1)=5` and
`n\:>\:1`