| Exam Board | Edexcel |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2010 |
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| Session | January |
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| Topic | Proof by induction |
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3. A sequence of numbers is defined by
$$\begin{aligned}
u _ { 1 } & = 2
u _ { n + 1 } & = 5 u _ { n } - 4 , \quad n \geqslant 1 .
\end{aligned}$$
Prove by induction that, for \(n \in \mathbb { Z } ^ { + } , u _ { n } = 5 ^ { n - 1 } + 1\).