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Solve the recurrence relation an = 2· an – 1 аn - 2 - a. What is the solution if the initial terms are ao = 4 and = 5 ? An b. What do the initial terms need to be for ag = 40 ? ao Aj = c. For which x are there initial terms which make ag = x ? ao

Solve the recurrence relation an = 2· an – 1 аn - 2 - a. What is the solution if the initial terms are ao = 4 and = 5 ? An b. What do the initial terms need to be for ag = 40 ? ao Aj = c. For which x are there initial terms which make ag = x ? ao

Advanced Engineering Mathematics
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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Solve the recurrence relation \( a_n = 2 \cdot a_{n-1} - a_{n-2} \). a. What is the solution if the initial terms are \( a_0 = 4 \) and \( a_1 = 5 \)? \[ a_n = \] b. What do the initial terms need to be for \( a_9 = 40 \)? \[ a_0 = \] \[ a_1 = \] c. For which \( x \) are there initial terms which make \( a_9 = x \)? \[ a_0 = \] \[ a_1 = \]
Transcribed Image Text:Solve the recurrence relation \( a_n = 2 \cdot a_{n-1} - a_{n-2} \). a. What is the solution if the initial terms are \( a_0 = 4 \) and \( a_1 = 5 \)? \[ a_n = \] b. What do the initial terms need to be for \( a_9 = 40 \)? \[ a_0 = \] \[ a_1 = \] c. For which \( x \) are there initial terms which make \( a_9 = x \)? \[ a_0 = \] \[ a_1 = \]
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