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Solve the recurrence defined by a for n ≥ 1. an 3(6^n)-2 3 and : 6an-1 + 5 an =

Solve the recurrence defined by a for n ≥ 1. an 3(6^n)-2 3 and : 6an-1 + 5 an =

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 13E
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Solve the recurrence defined by ao for n ≥ 1. an = 3(6^n)-2 = 3 and an = 6an-1 +5
Transcribed Image Text:Solve the recurrence defined by ao for n ≥ 1. an = 3(6^n)-2 = 3 and an = 6an-1 +5
Let {an} be a sequence defined by ao = 3, a₁ = 5 and There is a solution is of the form: an = an 9an-1 + 5an-2 for n ≥ 2 = = α₁(rı)” + a2(r2)" for suitable constants α₁, A2, T1, T2 with r₁ < 2. Find these constants. T1 = (-9-sqrt101)/2 12 = (-9+sqrt101)/2 α1 = (5+sqrt101)/(2sqrt101) α2 = (5-sqrt101)/(2sqrt101)
Transcribed Image Text:Let {an} be a sequence defined by ao = 3, a₁ = 5 and There is a solution is of the form: an = an 9an-1 + 5an-2 for n ≥ 2 = = α₁(rı)” + a2(r2)" for suitable constants α₁, A2, T1, T2 with r₁ < 2. Find these constants. T1 = (-9-sqrt101)/2 12 = (-9+sqrt101)/2 α1 = (5+sqrt101)/(2sqrt101) α2 = (5-sqrt101)/(2sqrt101)
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