| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Proof by induction |
| Type | Prove divisibility |
| Difficulty | Standard +0.3 This is a straightforward proof by induction for divisibility, requiring standard technique: verify base case n=1, assume for n=k, then show 13^(2k+1) + 8 is divisible by 7 using the inductive hypothesis. The algebraic manipulation is routine (factoring out 13² and using the hypothesis), making this easier than average for Further Maths students who have learned the induction template. |
| Spec | 4.01a Mathematical induction: construct proofs |
7. Prove, by mathematical induction, that $13 ^ { ( 2 n - 1 ) } + 8$ is a multiple of 7 for all positive integers $n$.\\
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\hfill \mbox{\textit{WJEC Further Unit 1 2024 Q7 [7]}}