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0580/32 May/Jun 2026, Question 15: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 3 marks

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The question, in short

A sequence has nth term 3n − 1. Find its first three terms, then identify which numbers from a given list belong to the sequence.

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Part (a) · 1 mark

Write down the first three terms of the sequence with nth term 3n − 1.

  1. 1n = 1: 3 × 1 − 1 = 2
  2. 2n = 2: 3 × 2 − 1 = 5
  3. 3n = 3: 3 × 3 − 1 = 8

Answer2, 5, 8

Part (b) · 2 marks

From 325 to 332, write down every number that is in the sequence with nth term 3n − 1.

  1. 1Terms are 1 less than a multiple of 3
  2. 23n − 1 = 326 gives n = 109
  3. 3329: n = 110; 332: n = 111
  4. 4In the sequence: 326, 329, 332

Answer326, 329, 332

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Also searched as: 0580/32/M/J/26 · 0580_s26_qp_32 · 0580 s26 32 · question 15.
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