3.4. A sequence s,, S2, S3, ... is defined recursively as follows: Sk = 5Sk-1 + (Sk-2)2 for all integers k 2 3 S1 = 4 S2 = 8 Use (strong) mathematical induction to prove that s, is divisible by 4 for all integers n 2 1. %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 40E
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3.4. A sequence s,, S2, S3, ... is defined recursively as follows:
Sk = 5Sk-1 + (Sk-2)² for all integers k 2 3
S1 = 4
S2 = 8
Use (strong) mathematical induction to prove that s, is divisible by 4 for all
integers n > 1.
Transcribed Image Text:3.4. A sequence s,, S2, S3, ... is defined recursively as follows: Sk = 5Sk-1 + (Sk-2)² for all integers k 2 3 S1 = 4 S2 = 8 Use (strong) mathematical induction to prove that s, is divisible by 4 for all integers n > 1.
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