Problem on deriving binet formula

Question

I'm trying to understand binet formula. I got a good explanation here. Please look at the link. Everything just fine but one thing. It said that $A_n = A_{n-1} + A_{n-2}$, which is fibonacci. But why $A_n = Cx^n$?

Answer 1

It is a guess. Many two term linear recurrence equations can be written in closed form.

Answer 2

It's recurrence relation. I think this explanation helps a lot.