| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Standard +0.3 This is a straightforward divisibility proof by induction with a simple algebraic structure. The inductive step requires factoring out 5^k and showing 5^k(5-1) + 8 is divisible by 4, which is routine manipulation. While it's a Further Maths topic, it's a standard textbook exercise requiring no novel insight, making it slightly easier than average overall. |
| Spec | 4.01a Mathematical induction: construct proofs |
\begin{enumerate}
\item Prove by induction that, for $n \in \mathbb { Z } ^ { + }$,
\end{enumerate}
$$\mathrm { f } ( n ) = 5 ^ { n } + 8 n + 3 \text { is divisible by } 4$$
\hfill \mbox{\textit{Edexcel F1 Q5 [6]}}