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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.

Power System Analysis and Design (MindTap Course List)
Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.22P
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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.
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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