Let r satisfy r2= r + 1. Show that the sequence an = Arn, where A is constant, satisfies the Fibonacci sequence an = an-1 + an-2 for n > 2.
The given equations above are the only relevant equations.
The Attempt at a Solution
I think have to show that Arn = Arn-1 + Arn-2, but I'm not sure how to manipulate the given equations to achieve such a thing. I can factor one side so that Arn = A(rn-1 + rn-2), and then say that rn = rn-1 + n-2, but I have no idea what to do from here.