| Exam Board | OCR |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2016 |
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| Session | June |
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| Topic | Proof by induction |
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5 The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$u _ { 1 } = 5 \text { and } u _ { n + 1 } = 3 u _ { n } + 2 \text { for } n \geqslant 1 \text {. }$$
Prove by induction that \(u _ { n } = 2 \times 3 ^ { n } - 1\).