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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
Transcribed Image Text: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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