(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

its given lol

3. 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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# Homework Help: Solving a recurrence relation

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