MathCastle
Proof Writing & Problem SolvingEasy

Proof Writing & Problem Solving · Easy problem

Define a1=3a_1 = 3 and an+1=2an−1a_{n+1} = 2a_n - 1 for n≥1n \ge 1. Induction proves an=2n+1a_n = 2^n + 1 (step: 2(2k+1)−1=2k+1+12(2^k + 1) - 1 = 2^{k+1} + 1). What is a10a_{10}?

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