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

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 

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

You need to show me the graphs so that i can choose one