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0580/12 Oct/Nov 2025, Question 27: The nth Term of a Linear Sequence

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 4 marks

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The question, in short

Sequence questions: find the nth term from the first four terms 2, 8, 14, 20, and find the first three terms of the sequence with nth term n² + 10.

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Part (a) · 2 marks

Find the nth term of the sequence whose first four terms are 2, 8, 14, 20.

  1. 1The terms go up by 6, so 6n
  2. 26 × 1 = 6, and 6 − 4 = 2
  3. 3nth term = 6n − 4

Answer6n − 4

Part (b) · 2 marks

Find the first three terms of the sequence whose nth term is n² + 10.

  1. 1n = 1: 1 + 10 = 11; n = 2: 4 + 10 = 14; n = 3: 9 + 10 = 19
  2. 211, 14, 19

Answer11, 14, 19

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