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Given the sequence defined with the recurrence relation: ao = 1 ak = 3k-ak-1 +1 for k ≥ 1 Using iteration, solve the recurrence relation when n ≥ 0 (i.e. find an analytic formula for an). Simplify your answer as much as possible, showing your work. In particular, your final answer should not contain Σ and II. You must show your work to get full marks. HINT: You should calculate the first few terms (i.e. a₁, az, a3) and keep the immediate answers to analyze the pattern before making a guess for an. Solutions in the exercises from the textbook also provide ideas of how to simplify your answer.

Given the sequence defined with the recurrence relation: ao = 1 ak = 3k-ak-1 +1 for k ≥ 1 Using iteration, solve the recurrence relation when n ≥ 0 (i.e. find an analytic formula for an). Simplify your answer as much as possible, showing your work. In particular, your final answer should not contain Σ and II. You must show your work to get full marks. HINT: You should calculate the first few terms (i.e. a₁, az, a3) and keep the immediate answers to analyze the pattern before making a guess for an. Solutions in the exercises from the textbook also provide ideas of how to simplify your answer.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 57EQ
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Given the sequence defined with the recurrence relation: ao = 1 ak = 3k-ak-1 +1 for k ≥ 1 Using iteration, solve the recurrence relation when n ≥ 0 (i.e. find an analytic formula for an). Simplify your answer as much as possible, showing your work. In particular, your final answer should not contain Σ and II. You must show your work to get full marks. HINT: You should calculate the first few terms (i.e. a₁, az, a3) and keep the immediate answers to analyze the pattern before making a guess for an. Solutions in the exercises from the textbook also provide ideas of how to simplify your answer.
Transcribed Image Text:Given the sequence defined with the recurrence relation: ao = 1 ak = 3k-ak-1 +1 for k ≥ 1 Using iteration, solve the recurrence relation when n ≥ 0 (i.e. find an analytic formula for an). Simplify your answer as much as possible, showing your work. In particular, your final answer should not contain Σ and II. You must show your work to get full marks. HINT: You should calculate the first few terms (i.e. a₁, az, a3) and keep the immediate answers to analyze the pattern before making a guess for an. Solutions in the exercises from the textbook also provide ideas of how to simplify your answer.
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