| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Standard +0.3 This is a standard Further Maths induction proof for divisibility. While it requires proper induction structure (base case, assumption, inductive step), the algebra is straightforward: factoring out 4^k from 4^(k+1) and manipulating 6(k+1) to show divisibility by 18. It's slightly easier than average because divisibility proofs follow a well-practiced template and the arithmetic manipulation is routine for Further Maths students. |
| Spec | 4.01a Mathematical induction: construct proofs |
\begin{enumerate}
\item Prove, by induction, that for $n \in \mathbb { Z } , n \geqslant 2$
\end{enumerate}
$$4 ^ { n } + 6 n - 10$$
is divisible by 18
\hfill \mbox{\textit{Edexcel F1 2023 Q9 [5]}}