Let ao, a1, a2, ... be a sequence of real numbers defined by the recurrence relation given below: do := 4 for each integer n > 1, an = 3an-1+4 Using a Proof by Induction prove that, for all integers n > 0, the nth term of the above sequence equals 5 – 5-". That is, prove the following statement P(n) holds true for all integers n > 0: P(n): а, 3D 5 — 5-т Important: Include all relevant details in your proof. If variables appear in your proof, clearly indicate what they represent. Clearly indicate your Induction Hypothesis and indicate exactly when it is used in the proof of your Induction Step.

Let ao, a1, a2, ... be a sequence of real numbers defined by the recurrence relation given below: do := 4 for each integer n > 1, an = 3an-1+4 Using a Proof by Induction prove that, for all integers n > 0, the nth term of the above sequence equals 5 – 5-". That is, prove the following statement P(n) holds true for all integers n > 0: P(n): а, 3D 5 — 5-т Important: Include all relevant details in your proof. If variables appear in your proof, clearly indicate what they represent. Clearly indicate your Induction Hypothesis and indicate exactly when it is used in the proof of your Induction Step.

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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Question

Let ao, a1, a2, ... be a sequence of real numbers defined by the recurrence relation given
below:
do := 4
for each integer n > 1,
an = 3an-1+4
Using a Proof by Induction prove that, for all integers n > 0, the nth term of the above
sequence equals 5 – 5-".
That is, prove the following statement P(n) holds true for all integers n > 0:
P(n): а, 3D 5 — 5-т
Important: Include all relevant details in your proof. If variables appear in your proof,
clearly indicate what they represent. Clearly indicate your Induction Hypothesis and indicate
exactly when it is used in the proof of your Induction Step.

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