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Possible Duplicate:
Does $x_{n+2} = (x_{n+1} + x_{n})/2$ converge?

i am asked to prove the convergence of this sequence. What given is, is this:
$a_{0}:=a$, and $a_{1}:=b$ and for all $n\ge2$ and it says that the sequence really converges, the task is to prove it. my doubt is whether i never use induction for convergence proof.

my steps:
$\frac{1}{2}(a_{n-1}+a_{n-2})=\frac{a_{n-1}}{2}+\frac{a_{n-2}}{2}=.. help ..=$ the sequence converges to something...

thanks for help and guidance

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