Suppose that g1, 92,93, ... is a sequence defined as follows: 91 = 3, 92 = 5, gk = 3gk-1 - 2gk-2 for each integer k > 3. %3D Prove that gn= 2" + 1 for every integer n > 1.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.1: Sequences And Their Notations
Problem 67SE: Consider the sequence defined by an=68n. Is an=421 a term in the sequence? Verify the result.
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Suppose that g1, 92, 93, ... is a sequence defined as follows:
91 = 3, 92 = 5, gk =
3gk-1 - 2gk-2 for each integer k 2 3.
%3D
Prove that g,n
= 2" + 1 for every integer n 2 1.
Transcribed Image Text:Suppose that g1, 92, 93, ... is a sequence defined as follows: 91 = 3, 92 = 5, gk = 3gk-1 - 2gk-2 for each integer k 2 3. %3D Prove that g,n = 2" + 1 for every integer n 2 1.
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