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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85a68bee-e492-4f07-94f8-32e724a354a8%2F328f0418-093e-411f-86d7-1cb9750ffce3%2F19wlisc_processed.jpeg&w=3840&q=75)
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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