Given the recursive sequence an = 3·an-1-2·an-2, where ao = 0, a₁ = 1, (a) Find a2, a3, a4, as, as using the recurrence relation. (b) Use either a shortcut (that we talked about in the notes) or iteration to obtain an explicit formula for an. If you use a shortcut, specify whether the recurrence sequence is arithmetic or geometric. If you use iteration, explain your reasoning. (c) What technique(s) could you use to prove that the explicit formula in (ii) true for all n ≥ 0?
Given the recursive sequence an = 3·an-1-2·an-2, where ao = 0, a₁ = 1, (a) Find a2, a3, a4, as, as using the recurrence relation. (b) Use either a shortcut (that we talked about in the notes) or iteration to obtain an explicit formula for an. If you use a shortcut, specify whether the recurrence sequence is arithmetic or geometric. If you use iteration, explain your reasoning. (c) What technique(s) could you use to prove that the explicit formula in (ii) true for all n ≥ 0?
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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Transcribed Image Text:Given the recursive sequence an = 3·an-1-2·an-2, where ao = 0, a₁ = 1,
(a) Find a2, a3, a4, as, as using the recurrence relation.
(b) Use either a shortcut (that we talked about in the notes) or iteration to obtain an explicit formula
for an. If you use a shortcut, specify whether the recurrence sequence is arithmetic or geometric.
If you use iteration, explain your reasoning.
(c) What technique(s) could you use to prove that the explicit formula in (ii) true for all n ≥ 0?
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