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n-1 hII ( f3i+1p – f3i-1h f3i-1p – fai-3h ) (無 f3i+29 – fzik ) Faq – fzi-zk ) X6n-4 | i=0 -1 = kII (* ( f3i+3P – fzi+1h f3i+1P – fzi-1h fai+19 – f3i-1k) f3i-19 – f3i-3k ) ' X6n-3 n-1 f3i+39 – f3i+1k fsi+19 – f3i-1k, f3i+2P - faih II X6n-2 f3ip – fai-zh) ) FaiP - i=0

n-1 hII ( f3i+1p – f3i-1h f3i-1p – fai-3h ) (無 f3i+29 – fzik ) Faq – fzi-zk ) X6n-4 | i=0 -1 = kII (* ( f3i+3P – fzi+1h f3i+1P – fzi-1h fai+19 – f3i-1k) f3i-19 – f3i-3k ) ' X6n-3 n-1 f3i+39 – f3i+1k fsi+19 – f3i-1k, f3i+2P - faih II X6n-2 f3ip – fai-zh) ) FaiP - i=0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 9E
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Theorem 5. Let {xn}4 be a solution of Eq.(9). Then for n = 0, 1, 2, ... n=-4 n-1 f3i+1P – f3i-1h` f3i-1p – fai-zh) \Fas9 – fai-2k ) ' fai+29 – fzik\ » X6n-4 i=0 п-1 fai+3P – fai+ih\ ( fai+19 – f3i–1k) Fsi+1P – fai-1h) (Fsi-19 – f3i-3k , X6n-3 i=0 n-1 ( fai+39 – fai+1k П X6n-2 f3iP – fai-zh) i=0 PI(si+4P – f3i+2h) fai+2P – faih п-1 ( f3i+29 – f3ik \f3:9 – fzi-2k ) X6n-1 i=0 п-1 fai+3P – fsi+1h \ f3i+1P – f3i-1h, (fsi+49 – fsi+2k fzi+29 – f3ik X6n i=0 п-1 ( fzi+5P – fzi+3h` П f3i+3P – fai+1h, fai+39 – f3i+1k` fsi+19 – fai-1k ) 2р — h X6n+1 р — h i=0 wherer-4 = h, x_3 = k, x_2 = r, x_1 = P, x0 = q, {fm}m=-1 = {-1, 1, 0, 1, 1, 2, 3, 5, 8, ...}.
Transcribed Image Text:Theorem 5. Let {xn}4 be a solution of Eq.(9). Then for n = 0, 1, 2, ... n=-4 n-1 f3i+1P – f3i-1h` f3i-1p – fai-zh) \Fas9 – fai-2k ) ' fai+29 – fzik\ » X6n-4 i=0 п-1 fai+3P – fai+ih\ ( fai+19 – f3i–1k) Fsi+1P – fai-1h) (Fsi-19 – f3i-3k , X6n-3 i=0 n-1 ( fai+39 – fai+1k П X6n-2 f3iP – fai-zh) i=0 PI(si+4P – f3i+2h) fai+2P – faih п-1 ( f3i+29 – f3ik \f3:9 – fzi-2k ) X6n-1 i=0 п-1 fai+3P – fsi+1h \ f3i+1P – f3i-1h, (fsi+49 – fsi+2k fzi+29 – f3ik X6n i=0 п-1 ( fzi+5P – fzi+3h` П f3i+3P – fai+1h, fai+39 – f3i+1k` fsi+19 – fai-1k ) 2р — h X6n+1 р — h i=0 wherer-4 = h, x_3 = k, x_2 = r, x_1 = P, x0 = q, {fm}m=-1 = {-1, 1, 0, 1, 1, 2, 3, 5, 8, ...}.
Bxn-1n-2 YIn-1 + 8xn-4 Xn+1 = axn-2 + n = 0, 1, .., (1) A specific form of the solutions of the difference equation has been provided Xn-1Xn-2 Xn+1 = xn-2+ (9) Xn-1 - Xn-4 where the initial conditions x-4, x_3, x-2, x-1, xo are arbitrary non zero real num- bers with x_4 7 x-1-
Transcribed Image Text:Bxn-1n-2 YIn-1 + 8xn-4 Xn+1 = axn-2 + n = 0, 1, .., (1) A specific form of the solutions of the difference equation has been provided Xn-1Xn-2 Xn+1 = xn-2+ (9) Xn-1 - Xn-4 where the initial conditions x-4, x_3, x-2, x-1, xo are arbitrary non zero real num- bers with x_4 7 x-1-
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