- #1

Illania

- 26

- 0

## Homework Statement

The problem:

Let r satisfy r

^{2}= r + 1. Show that the sequence a

_{n}= Ar

^{n}, where A is constant, satisfies the Fibonacci sequence a

_{n}= a

_{n-1}+ a

_{n-2}for n > 2.

## Homework Equations

The given equations above are the only relevant equations.

## The Attempt at a Solution

I think have to show that Ar

^{n}= Ar

^{n-1}+ Ar

^{n-2}, but I'm not sure how to manipulate the given equations to achieve such a thing. I can factor one side so that Ar

^{n}= A(r

^{n-1}+ r

^{n-2}), and then say that r

^{n}= r

^{n-1}+

^{n-2}, but I have no idea what to do from here.