A Coupled Linear System

★ 7/10Limits calculus Recursion sequences

Problem

Sequences $\{a_n\}$ and $\{b_n\}$ satisfy $b_1 = 2a_1 = 4$ and

\begin{cases} a_{n+1} = -a_n - 2b_n, \\ b_{n+1} = 6(a_n + b_n), \end{cases} \qquad n \in \mathbb{N}^*.

1. Find closed formulas for $a_n$ and $b_n$ . 2. Find $\displaystyle\lim_{n \to \infty} \frac{a_n}{b_n}$ .

Answer

Solution

Difficulty	7/10
Topics	Limits, calculus, Recursion, sequences

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