A Difference Argument

★ 8/10Arithmetic Progression Monotonicity sequences

Problem

Sequences $\{a_n\}$ , $\{b_n\}$ , $\{c_n\}$ satisfy

b_n = a_n - a_{n+2}, \qquad c_n = a_n + 2a_{n+1} + 3a_{n+2}.

If $\{c_n\}$ is an arithmetic sequence and $b_n \leqslant b_{n+1}$ for all $n$ , prove that $\{a_n\}$ is an arithmetic sequence.

Answer

Solution

Difficulty	8/10
Topics	Arithmetic Progression, Monotonicity, sequences

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