| Exam Board | AQA |
|---|
| Module | Further Paper 1 (Further Paper 1) |
|---|
| Year | 2024 |
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| Session | June |
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| Topic | Proof by induction |
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6 The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
u _ { 1 } & = 1
u _ { n + 1 } & = u _ { n } + 3 n
\end{aligned}$$
Prove by induction that for all integers \(n \geq 1\)
$$u _ { n } = \frac { 3 } { 2 } n ^ { 2 } - \frac { 3 } { 2 } n + 1$$