how do you do induction proofs with sequences?

https://imgur.com/a/jNeZBAu

I think I did the base case right, I got 1/4 = 1/4.

However I am confused with the induction step. I replaced all k’s with k+1 and got

a(k+3) = 0.5(a(k+1) + a(k+2))

Are you supposed to substitute (k+3) in the a(n) formula, and do that for (k+1) and (k+2), then see if both sides of the equation are equivalent?