A Parameterized Linear Recursion

★ 7/10Quadratic Equations Recursion sequences inequality Casework

Problem

In a sequence $\{a_n\}$ , $a_1 = 1$ and

a_{n+1} = ca_n + c^{n+1}(2n+1), \qquad n \in \mathbb{N}^*,

where $c \neq 0$ is real.

1. Find a formula for $a_n$ . 2. If $a_{2k} > a_{2k-1}$ for every $k \in \mathbb{N}^*$ , find the range of possible values of $c$ .

Answer

Solution

Difficulty	7/10
Topics	Quadratic Equations, Recursion, sequences, inequality, Casework

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