9231 P12 - Nov 2024 - Q01
4143
The sequence \(u_1, u_2, u_3, \ldots\) is such that \(u_1 = 4\) and \(u_{n+1} = 3u_n - 2\) for \(n \geq 1\).
Prove by induction that \(u_n = 3^n + 1\) for all positive integers \(n\).
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