Finding closed form of sequence.

[12base]

Homework Statement

{U_0 = 9, U_1 = -3}

U_(n+2) = -(5/4) U_(n+1) + (3/8) U_(n)

Homework Equations

The Attempt at a Solution

First step was to attempt to find the common difference by trying to find the 3rd term:

U_(2) = -(5/4) u_(1) + 3/8 U_(0) = -(57/8)

This does not give a common difference, I was expecting -1/3

I feel I have gone wrong somewhere, help would be greatly appreciated!

 

[pasmith]

Homework Statement

{U_0 = 9, U_1 = -3}

U_(n+2) = -(5/4) U_(n+1) + (3/8) U_(n)

Homework Equations

The Attempt at a Solution

First step was to attempt to find the common difference by trying to find the 3rd term:

U_(2) = -(5/4) u_(1) + 3/8 U_(0) = -(57/8)

You have a sign error; (-5/4)(-3) + (3/8)(9) = 57/8.

This does not give a common difference,

Why do you expect it to?

The method of solving such linear recurrence relations is to look for a solution of the form $u_n = A\lambda_1^n + B\lambda_2^n$. If you substitute this into the recurrence relation you will find that $\lambda_1$ and $\lambda_2$ are solutions of the same quadratic equation. The given values for $u_0$ and $u_1$ will then enable you to find $A$ and $B$.