Question

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

Answer 1

Answer:

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

Step-by-step 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 $n\:>\:1$