Question

What recursive formula can be used to generate the sequence `5, -1, -7, -13, -19`, where `f(1) = 5` and `n>1`?

Answer 1

`a_n=a_(n-1)-6`

Explanation:

Well, we can start off by looking at the relationship between the numbers.

Note that each number in the sequence is decreasing by 6, therefore the common difference is -6.

A recursive formula defines terms in a sequence in relation to previous numbers.

The standard formula is as follows:

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

All you have to do is substitute -6 for `d`:

`a_n=a_(n-1)-6`

And there you have it.