11. Let (an) be the sequence defined recursively by, a1 = 3, a2 = 4, for n > 3, an 2ап-1 + аn-2. Show that for all n, an is even if and only if n is.

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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Use Inductive method:

11. Let (an) be the sequence defined recursively by,
a1 = 3,
a2 = 4,
for n > 3, an = 2an-1 + ɑn-2.
Show that for all n, an is even if and only if n is.
Transcribed Image Text:11. Let (an) be the sequence defined recursively by, a1 = 3, a2 = 4, for n > 3, an = 2an-1 + ɑn-2. Show that for all n, an is even if and only if n is.
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