I take it you mean (If you don't want to use Latex, use parentheses: (n+1)a_(n+1)+ a_(n-1)= 0.
And I think you mean
Please do not mix "n" and "N"!
Now, do you know what induction is? If so, what have you tried to do and where do you have a problem?
Have you checked that, when n= 1, ?