please help me with this Given a sequence (xn; n ≥ 0) satisfying n= 16xn-1 − 64xn-2 + 2³n+2, n ≥ 2 with x = 4, x₁ = 8.(a) Find explicitly the general term n of the sequence in terms of n.(b) Find the ordinary generating function of the sequence in a form of rational functions.(c) Transform the linear recurrence equation of the sequence into a matrix form.

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Given a sequence (xn; n ≥ 0) satisfying n = 16xn-1 - 64xn-2 +2³n+2, n ≥ 2 with xo = 4,1 = 8. (a) Find explicitly the general term n of the sequence in terms of n.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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please help me with this

Given a sequence (xn; n ≥ 0) satisfying n= 16xn-1 − 64xn-2 + 2³n+2, n ≥ 2 with x = 4, x₁ = 8.
(a) Find explicitly the general term n of the sequence in terms of n.
(b) Find the ordinary generating function of the sequence in a form of rational functions.
(c) Transform the linear recurrence equation of the sequence into a matrix form.

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