SPS SPS FM 2026 November — Question 8 5 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2026
SessionNovember
Marks5
TopicProof by induction
TypeProve divisibility
DifficultyModerate -0.3 This is a straightforward proof by induction with a simple divisibility statement. The base case is trivial (7×1-15=-8, divisible by 4), and the inductive step requires only basic algebra to show 7×9^(k+1)-15 = 9(7×9^k-15)+120, both terms divisible by 4. While it tests understanding of induction structure, it requires no novel insight and is mechanically simpler than average A-level proof questions.
Spec4.01a Mathematical induction: construct proofs

Prove by induction that \(7 \times 9^n - 15\) is divisible by \(4\), for all integers \(n \geq 0\). [5]

Prove by induction that $7 \times 9^n - 15$ is divisible by $4$, for all integers $n \geq 0$.
[5]

\hfill \mbox{\textit{SPS SPS FM 2026 Q8 [5]}}