| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2011 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof by induction |
4 It is given that $\mathrm { f } ( n ) = 3 ^ { 3 n } + 6 ^ { n - 1 }$.\\
(i) Show that $\mathrm { f } ( n + 1 ) + \mathrm { f } ( n ) = 28 \left( 3 ^ { 3 n } \right) + 7 \left( 6 ^ { n - 1 } \right)$.\\
(ii) Hence, or otherwise, prove by mathematical induction that $\mathrm { f } ( n )$ is divisible by 7 for every positive integer $n$.
\hfill \mbox{\textit{CAIE FP1 2011 Q4}}