| Exam Board | OCR |
|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
|---|
| Year | 2018 |
|---|
| Session | September |
|---|
| Topic | Proof by induction |
|---|
3 A sequence is defined by \(a _ { 1 } = 6\) and \(a _ { n + 1 } = 5 a _ { n } - 2\) for \(n \geqslant 1\).
Prove by induction that for all integers \(n \geqslant 1 , a _ { n } = \frac { 11 \times 5 ^ { n - 1 } + 1 } { 2 }\).