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Consider the following linear non-homogeneous recurrence relation where go = 1, g, = 3 and g,+1 = 7g, - 10g, -1+ n2 - n+1 for 1 2 1. The reduced closed form of g, can be represented as g, = (P x p" + Q x q" + Rn² + Sn + T) where p and q are the solutions of the characteristic equation of the recurrence. Given that, p is smaller than q. Here, P, Q, R, S, T, A are all integers. What is the value of P? Nhat is the value of Q??

Consider the following linear non-homogeneous recurrence relation where go = 1, g, = 3 and g,+1 = 7g, - 10g, -1+ n2 - n+1 for 1 2 1. The reduced closed form of g, can be represented as g, = (P x p" + Q x q" + Rn² + Sn + T) where p and q are the solutions of the characteristic equation of the recurrence. Given that, p is smaller than q. Here, P, Q, R, S, T, A are all integers. What is the value of P? Nhat is the value of Q??

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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Consider the following linear non-homogeneous recurrence relation where go = 1, g, = 3 and g,+1 = 7g, - 10g, -1+ n2 - n + 1 for nz 1. The reduced closed form of g, can be represented as g, = + Qx q" + Rn2 + Sn + T) where p and q are the solutions of the characteristic equation of the recurrence. Given that, p is smaller than q. Here, P, Q, R, S, T, A are all integers. What is the value of P? What is the value of Q?? What is the value of R? What is the value of T?
Transcribed Image Text:Consider the following linear non-homogeneous recurrence relation where go = 1, g, = 3 and g,+1 = 7g, - 10g, -1+ n2 - n + 1 for nz 1. The reduced closed form of g, can be represented as g, = + Qx q" + Rn2 + Sn + T) where p and q are the solutions of the characteristic equation of the recurrence. Given that, p is smaller than q. Here, P, Q, R, S, T, A are all integers. What is the value of P? What is the value of Q?? What is the value of R? What is the value of T?
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