| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Moderate -0.3 This is a straightforward divisibility proof by induction with a simple algebraic manipulation. The inductive step requires factoring out 7^k and recognizing that 7-2=5 provides the divisibility, which is a standard technique. While it's a Further Maths question, it's one of the most routine types of induction proofs with no conceptual surprises, 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}
$$f ( n ) = 7 ^ { n } - 2 ^ { n } \text { is divisible by } 5$$
\hfill \mbox{\textit{Edexcel F1 2014 Q9 [6]}}