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4024/12 May/Jun 2026, Question 13: Sequences and nth term

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

Work with sequences: list terms from the rule n + 8; for 4, 10, 16, 22 give the term-to-term rule and nth term Tₙ; then if Rₙ = Tₙ/(n + 8) and the kth term of R equals 5, find k.

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Part (a) · 1 mark

First three terms of n + 8.

  1. 1n = 1: 1 + 8 = 9
  2. 2n = 2: 10, n = 3: 11

Answer9, 10, 11

Part (bi) · 1 mark

  1. 110 − 4 = 16 − 10 = 22 − 16 = 6
  2. 2Rule: add 6

Answeradd 6

Part (bii) · 2 marks

  1. 1Common difference 6, so 6n
  2. 26 × 1 = 6, and 6 − 2 = 4
  3. 3Tₙ = 6n − 2

Answer6n − 2

Part (c) · 3 marks

Find k when (kth term of T) ÷ (k + 8) = 5.

  1. 1(6k − 2)/(k + 8) = 5
  2. 26k − 2 = 5(k + 8) = 5k + 40
  3. 3k = 42

Answer42

Stuck on a step? Read the free lesson: Solving Linear Equations

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Also searched as: 4024/12/M/J/26 · 4024_s26_qp_12 · 4024 s26 12 · question 13.
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