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