A sequence is defined recursively by the formula f(n + 1) = f(n) + 3 . The first term of the sequence is –4. What is the next term in the sequence?

Question

kainui · Answer

$f(n)$ is any term in the sequence, it's just waiting for you to ask for a specific one in it. So if you want the first one in the sequence, then n=1 because 1 is the first number. So when we plug it in we have:

$f(1)=-4$

Which is what they said, the first term is -4 when we asked. Now what's the next term? That'll be when n=2, so what's $f(2)=?$ Well, we use that formula they give us to find out, plug in n=1 and see what you get for $f(n+1)$ and $f(n)$ and think about it.

$$f(n+1)=f(n)+3$$