Question

What is the recursive formula for the sequence {−4,−1,2,5,…}?

A. f(1)=−4 and f(n+1)=−4+3

B. f(1)=−4 and f(n+1)=f(n)+3

C. f(1)=−4 and f(n)=f(n+1)+3

D. f(1)=0 and f(n+1)=f(n)−4

Answer 1

The first term is -4, so the recursive formula must start with

`f(1)=-4`

Then, as you can see, each term is 3 more than the previous one, so the recursive relation is

`f(n+1)=f(n)+3`

which literally means "the next term is the previous one plus three".