Consider the following linear non-homogeneous recurrence relation where g0=1,g1=3 and gn+1=7gn−10gn−1+2n−3 for n≥1. The reduced closed form of gn can be represented as gn=1/A(P×pn+Q×qn+Rn+S) 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,A are all integers. 1. What is the value of P? 2. What is the value of Q?? 3. What is the value of R+S? 4. What is the value of A?

Consider the following linear non-homogeneous recurrence relation where g0=1,g1=3 and gn+1=7gn−10gn−1+2n−3 for n≥1. The reduced closed form of gn can be represented as gn=1/A(P×pn+Q×qn+Rn+S) 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,A are all integers. 1. What is the value of P? 2. What is the value of Q?? 3. What is the value of R+S? 4. What is the value of A?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 40E

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Question

Consider the following linear non-homogeneous recurrence relation where g₀=1,g₁=3 and g_n+1=7g_n−10g_n−1+2n−3 for n≥1. The reduced closed form of g_n can be represented as g_n=1/A(P×pⁿ+Q×qⁿ+Rn+S) 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,A are all integers.

1. What is the value of P?

2. What is the value of Q??

3. What is the value of R+S?

4. What is the value of A?

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