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0580/21 May/Jun 2026, Question 11: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 6 marks

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The question, in short

Sequences A, B and C are linear, with Cₙ = Aₙ + Bₙ and Bₙ = n − 5; use the table to work out Aₙ, then handle a separate sequence 1/2, 1, 2, 4, 8.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

Use Cₙ = Aₙ + Bₙ and Bₙ = n − 5 to work out the nth term of sequence A.

  1. 1C goes up by 3: Cₙ = 3n − 4
  2. 2Aₙ = Cₙ − Bₙ = 3n − 4 − (n − 5)
  3. 3Aₙ = 2n + 1

Answer2n + 1

Part (bi) · 1 mark

Find the next term of the sequence 1/2, 1, 2, 4, 8.

  1. 1Each term is double the previous
  2. 28 × 2 = 16

Answer16

Part (bii) · 2 marks

Find the nth term of the sequence 1/2, 1, 2, 4, 8.

  1. 1Terms are powers of 2: 2⁻¹, 2⁰, 2¹, 2², 2³
  2. 2The power is 2 less than n
  3. 3nth term = 2ⁿ⁻²

Answer2ⁿ⁻²

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