Use Inductive method: 10. Let (an) be the sequence defined recursively by,a1 = -1,a2 = 7,for n 2 3, an— ап-1 +2ап-2.Show that for all n, am =2" + 3(-1)".

Name: Use Inductive method: 10. Let (an) be the sequence defined recursively
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Description: Use Inductive method: 10. Let (an) be the sequence defined recursively by,a1 = -1,a2 = 7,for n 2 3, an— ап-1 +2ап-2.Show that for all n, am =2" + 3(-1)".

It is required to show that, an=2n+3(-1)n for all n. Let us check for n=1. a1=21+3(-1)1 -1=2-3…

Answered: 10. Let (an) be the sequence defined…

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10. Let (an) be the sequence defined recursively by, a1 = –1, a2 = 7, for n > 3, an = аn-1 + 2ап-2. Show that for all n, an = 2" +3(-1)".

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.2: Sequences, Series And Summation Notation

Problem 42E

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