c) Consider the pair of coupled first order difference equations g(n+1) = f(n), f(n + 1) = 8f(n) — 16g(n) + 36, where n is an integer > 1. (i) Find the associated second order difference equation for f. (ii) Hence find the direct prescriptions for f(n) and g(n) if f(1) = 36, and g(1) = 9.
c) Consider the pair of coupled first order difference equations g(n+1) = f(n), f(n + 1) = 8f(n) — 16g(n) + 36, where n is an integer > 1. (i) Find the associated second order difference equation for f. (ii) Hence find the direct prescriptions for f(n) and g(n) if f(1) = 36, and g(1) = 9.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question
maths help can you do c) please
![(a) Consider the sequence f(n) = 2 + 3n, where n is an integer ≥ 1.
(i) Evaluate the first six terms and sketch the graph of the sequence.
(ii) Find the recursive prescription of the sequence.
(b) (Using the method of trying a solution of the form f(n) = Kw", etc.,...) find the direct
prescription for the following recursively-prescribed sequence
f(n+2) − 2f(n+1) — 15f(n) = 0, where n is an integer ≥ 1, f(1) = 5, and f(2)= -95.
(c) Consider the pair of coupled first order difference equations
g(n+1) = f(n),
f(n + 1) = 8f(n) — 16g(n) + 36,
where n is an integer > 1.
Find the associated second order difference equation for f.
(ii) Hence find the direct prescriptions for f(n) and g(n) if f(1) = 36, and g(1) = 9.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffcd79c20-bd8e-42e5-9f71-d4c14c2616bc%2F8a13dbad-e3a7-4bf3-867f-51c8c6b2b571%2Fjludtwn_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Consider the sequence f(n) = 2 + 3n, where n is an integer ≥ 1.
(i) Evaluate the first six terms and sketch the graph of the sequence.
(ii) Find the recursive prescription of the sequence.
(b) (Using the method of trying a solution of the form f(n) = Kw", etc.,...) find the direct
prescription for the following recursively-prescribed sequence
f(n+2) − 2f(n+1) — 15f(n) = 0, where n is an integer ≥ 1, f(1) = 5, and f(2)= -95.
(c) Consider the pair of coupled first order difference equations
g(n+1) = f(n),
f(n + 1) = 8f(n) — 16g(n) + 36,
where n is an integer > 1.
Find the associated second order difference equation for f.
(ii) Hence find the direct prescriptions for f(n) and g(n) if f(1) = 36, and g(1) = 9.
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