Escaping Past $m$

★ 6/10Quadratic Equations Recursion algebra sequences Vieta's Formulas

Problem

A recursive sequence $\{x_n\}$ satisfies

x_{n+1} = x_n^2 - 4x_n, \quad n = 1, 2, \dots

Suppose that for every first term $x_1 \in \mathbb{R}$ with $x_1 \neq 0$ , the sequence always contains some term $x_k \geqslant m$ . Find the maximum possible value of $m$ .

Answer

Solution

Difficulty	6/10
Topics	Quadratic Equations, Recursion, algebra, sequences, Vieta's Formulas

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