A Linear System Limit

★ 8/10Geometric Progression Limits Recursion sequences

Problem

Sequences $\{x_n\}, \{y_n\}$ satisfy $x_0 = 5$ , $y_0 = 2$ , and

x_{n+1} = -\frac{7}{2}x_n + 6y_n, \qquad y_{n+1} = -3x_n + 5y_n.

Find $\lim_{n\to\infty} x_n$ and $\lim_{n\to\infty} y_n$ .

Answer

Solution

Difficulty	8/10
Topics	Geometric Progression, Limits, Recursion, sequences

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