| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Standard +0.3 This is a standard divisibility proof by induction with straightforward algebra. The base case is trivial (n=1 gives 1+512=513=57×9), and the inductive step requires factoring out 7^k + 8^(2k+1) and showing the remainder 6·7^k + 63·8^(2k+1) = 57(7^(k-1) + 8^(2k+1)) is divisible by 57. While it requires careful algebraic manipulation, it follows the standard template for such proofs without requiring novel insight. |
| Spec | 4.01a Mathematical induction: construct proofs |
\begin{enumerate}
\item Prove by induction that for $n \in \mathbb { Z } ^ { + }$
\end{enumerate}
$$f ( n ) = 7 ^ { n - 1 } + 8 ^ { 2 n + 1 }$$
is divisible by 57\\
(6)
\hfill \mbox{\textit{Edexcel F1 2024 Q8 [6]}}