| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2025 |
| Session | September |
| Marks | 5 |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Standard +0.3 This is a straightforward proof by induction with divisibility. The base case is trivial (n=0 gives 11-1-1=9), and the inductive step requires standard algebraic manipulation to factor out 3. While it's a Further Maths question, it follows a completely standard template with no conceptual surprises, making it slightly easier than average overall. |
| Spec | 4.01a Mathematical induction: construct proofs |
Prove by induction that $11 \times 7^n - 13^n - 1$ is divisible by 3, for all integers $n \geq 0$. [5]
\hfill \mbox{\textit{SPS SPS FM Pure 2025 Q2 [5]}}