| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Moderate -0.3 This is a straightforward proof by induction with a simple divisibility statement. The base case is trivial (n=1 gives 7+1=8), and the inductive step requires only basic algebraic manipulation to show 7^(k+1) + 3^k = 7(7^k + 3^(k-1)) - 4ยท3^(k-1), making the factor of 4 immediately apparent. While it's a Further Maths topic, it's a standard textbook exercise requiring no novel insight, making it slightly easier than an average A-level question. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps |
3 Prove by induction that, for all positive integers $n , 7 ^ { n } + 3 ^ { n - 1 }$ is a multiple of 4.
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q3 [5]}}