Hi everyone!

I'm not sure what to do with this induction question, can anyone help me please?

Let a_1=0, a_2=3, and, for all n>=3 let

a_n= 1/2(a_(n-1) + a_(n-2))

By induction on n, show that for all n>=2,

a_n= 2 + 4(-1/2)^n.

What I did so far was work with the 2nd equation, and said:

let n=1

0= 2 + 4(-1/2)^1

= 2 - 2

=0

therefore it is true for n=1

Assume true for n=k

a_k= 2 + 4(-1/2)^k

...what's the next step for the proof?Or have I gone completely wrong from the beginning?? Thanks in advance for your help guys!