Question

Find the first 4 terms of the Arithmetic sequence. f(n) = f(n-1) + 5 f(1) = -2

Answer 1

f(n) = f(n-1) + 5   simply means

the next term or f(n), will have a value of
the one before it, or f(n-1), +5

so.. you're looking for the 4th term, that means f(4)
to get 4th term then, that will be the 3rd term plus 5,
whatever the 3rd term is

now... f(1) = -2, simply means, the term 1, or f(1), or first term, is -2

now to find a term value in an arithmetic sequence $\bf f(n)=f(1)+(n-1)d\\\\ \begin{cases} n=n^{th}\ term\to &4\\ f(1)=\textit{first term}\to &-2\\ d= \begin{array}{llll} \textit{common difference, or amount}\\ \textit{added to get the next term} \end{array}\to &5 \end{cases}\\\\ -----------------------------\\\\ thus \\\\ f(4)=f(1)+(4-1)5$

and I'm sure you know what f(1) is, so, just plug it in, to get f(4), or 4th term