Consider the sequence (xn)n, n E NU{0} defined recursively as Xn = 7xn-1 – 10xn-2, xo = 2, x1 = 3. Show that the nth term is given by the closed formula 1 Xn 3 (7 - 2" – 3"). %3D
Consider the sequence (xn)n, n E NU{0} defined recursively as Xn = 7xn-1 – 10xn-2, xo = 2, x1 = 3. Show that the nth term is given by the closed formula 1 Xn 3 (7 - 2" – 3"). %3D
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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![(b) Consider the sequence \((x_n)_n\), \(n \in \mathbb{N} \cup \{0\}\) defined recursively as
\[ x_n = 7x_{n-1} - 10x_{n-2}, \quad x_0 = 2, \, x_1 = 3. \]
Show that the \(n\)th term is given by the closed formula
\[ x_n = \frac{1}{3} \left( 7 \cdot 2^n - 3^n \right). \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05f71249-0159-4369-afdd-b84b5bf21c00%2F48786c8c-0b68-468d-adb6-49c75d827f8b%2Fju2tvcn_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Consider the sequence \((x_n)_n\), \(n \in \mathbb{N} \cup \{0\}\) defined recursively as
\[ x_n = 7x_{n-1} - 10x_{n-2}, \quad x_0 = 2, \, x_1 = 3. \]
Show that the \(n\)th term is given by the closed formula
\[ x_n = \frac{1}{3} \left( 7 \cdot 2^n - 3^n \right). \]
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