| Exam Board | SPS |
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| Module | SPS FM Pure (SPS FM Pure) |
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| Year | 2023 |
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| Session | September |
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| Topic | Proof by induction |
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2. A sequence \(u _ { n }\) is defined by \(u _ { n + 1 } = 2 u _ { n } + 3\) and \(u _ { 1 } = 1\).
Prove by induction that \(u _ { n } = 4 \times 2 ^ { n - 1 } - 3\) for all positive integers \(n\).
[0pt]
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