| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Standard +0.3 This is a standard proof by induction for divisibility with straightforward algebra. While it's Further Maths content, the technique is routine: verify base case, assume for n=k, then show 4^(k+2) + 5^(2k+1) is divisible by 21 using the inductive hypothesis. The algebraic manipulation (factoring out 4 and 25) follows a well-practiced pattern for this question type, making it slightly easier than average overall. |
| Spec | 4.01a Mathematical induction: construct proofs |
9. Prove by induction that, for $n \in \mathbb { Z } ^ { + }$
$$f ( n ) = 4 ^ { n + 1 } + 5 ^ { 2 n - 1 }$$
is divisible by 21\\
\hfill \mbox{\textit{Edexcel F1 2016 Q9 [6]}}