| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2002 |
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| Session | November |
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| Topic | Proof by induction |
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3 It is given that, for \(n = 0,1,2,3 , \ldots\),
$$a _ { n } = 17 ^ { 2 n } + 3 ( 9 ) ^ { n } + 20$$
Simplify \(a _ { n + 1 } - a _ { n }\), and hence prove by induction that \(a _ { n }\) is divisible by 24 for all \(n \geqslant 0\).