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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Transcript:**
11. Let \((a_n)\) be the sequence defined recursively by,
\[ a_1 = 3, \]
\[ a_2 = 4, \]
for \( n \geq 3 \), \( a_n = 2a_{n-1} + a_{n-2} \).
Show that for all \( n \), \( a_n \) is even if and only if \( n \) is.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63f643a6-d37e-4098-8dc7-7802480db8dc%2F08f84127-2097-44b5-9a67-d35a86dbe388%2Fr2f675_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcript:**
11. Let \((a_n)\) be the sequence defined recursively by,
\[ a_1 = 3, \]
\[ a_2 = 4, \]
for \( n \geq 3 \), \( a_n = 2a_{n-1} + a_{n-2} \).
Show that for all \( n \), \( a_n \) is even if and only if \( n \) is.
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