- #1

silvermane

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## Homework Statement

Solve the recurrence relation

a

_{n}= 5a

_{n−1}− 3a

_{n−2}− 9a

_{n−3}for n ≥ 3

with initial values a

_{0}= 0, a

_{1}= 11, and a

_{2}= 34.

## Homework Equations

its given lol

## The Attempt at a Solution

I found that the characteristic equation for this rr is x

^{3}- 5x

^{2}+ 3x + 9 and found that the characteristic roots are 3, 3, -1...because we have 2 indistinct roots, I multiplied one of the 3 terms by n to get

a

_{n}= r3

^{n}+ sn3

^{n}- t

and so plugging back into the give rr we have

r3

^{n}+ sn3

^{n}- t = 5(r3

^{n-1}+ s(n-1)3

^{n-1}- t) - 3(r3

^{n-2}+ s(n-2)3

^{n-2}- t) - 9(r3

^{n-3}+ s(n-3)3

^{n-3}- t)

I'm thinking that in order to solve this, we're going to have to set this up as a system of equations, but I'm not sure how to do that with what I have. Any hints/tips/ suggestions on where to go next would be very helpful.

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