Alternating Couplings

★ 6/10Geometric Progression sequences Symmetry

Problem

Sequences $\{a_n\}, \{b_n\}$ satisfy $a_1 = b_1 = 1$ and

a_n + b_{n+1} = 2n, \qquad a_{n+1} + b_n = 2^n.

Let $S_n$ be the sum of the first $n$ terms of $\{a_n + b_n\}$ . Find $S_7$ .

Answer

Solution

Difficulty	6/10
Topics	Geometric Progression, sequences, Symmetry

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