Consider the sequence defined recursively as follows, ao = 2 and ar = 4ak-1+1, for all k > 1. 1. Find a1, a2, a3, a4, a5. 2. Show by induction that for all n 2 0, 7 x 4" – 1 an = 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the sequence defined recursively as follows,
ao = 2 and ak = 4ak–1+ 1,
for all k > 1.
1. Find a1, a2, a3, a4, ɑ5.
2. Show by induction that for all n > 0,
7 x 4" – 1
an =
3
Transcribed Image Text:Consider the sequence defined recursively as follows, ao = 2 and ak = 4ak–1+ 1, for all k > 1. 1. Find a1, a2, a3, a4, ɑ5. 2. Show by induction that for all n > 0, 7 x 4" – 1 an = 3
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