| Exam Board | SPS |
|---|
| Module | SPS FM Pure (SPS FM Pure) |
|---|
| Year | 2023 |
|---|
| Session | November |
|---|
| Topic | Proof by induction |
|---|
4. 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 \(n \in \mathbb { Z } ^ { + } , u _ { n } = 5 ^ { n - 1 } + 1\).
[0pt]
[BLANK PAGE]