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## Homework Statement

Let a

_{1}=2, a

_{2}=0, a

_{3}=-14 and a

_{n+1}=9a

_{n}-23a

_{n-1}+15a

_{n-2}for n>= 3. Show by induction that a

_{n}=3

^{n-1}-5

^{n-1}+2 for n>=1.

## Homework Equations

## The Attempt at a Solution

Ok this is annoying to type...

Base Case is true, which is the easy part.

The induction part I am not going to list all the steps since it is a pain in the bum to write it out so here it is where I got stuck (it might be wrong too :P):

3

^{n}-5

^{n}+2 = a

_{n+1}=9a

_{n}-23a

_{n-1}+15a

_{n-2}

What do I do thanks?