OCR FP1 AS 2021 June — Question 4 6 marks

Exam BoardOCR
ModuleFP1 AS (Further Pure 1 AS)
Year2021
SessionJune
Marks6
TopicProof by induction
TypeProve divisibility
DifficultyStandard +0.3 This is a standard proof by induction with divisibility, a core FP1 topic. The algebraic manipulation in the inductive step (factoring out 7 from 2·2^{n+1} + 5·9·9^n - 7·5·9^n) is straightforward once students recognize the standard technique. While it requires careful algebraic handling, it's a routine application of the induction framework with no novel insight needed, making it slightly easier than average.
Spec4.01a Mathematical induction: construct proofs

Prove by induction that \(2^{n+1} + 5 \times 9^n\) is divisible by 7 for all integers \(n \geq 1\). [6]

Prove by induction that $2^{n+1} + 5 \times 9^n$ is divisible by 7 for all integers $n \geq 1$. [6]

\hfill \mbox{\textit{OCR FP1 AS 2021 Q4 [6]}}