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0580/22 Feb/Mar 2024, Question 8: Quadratic and Cubic Sequences

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 4 marks

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The question, in short

Two sequence questions: use the rule n² − 3 to generate the first three terms, and find the nth term rule for the sequence 1, 3, 9, 27, 81.

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Part (a) · 2 marks

Substitute n = 1, 2 and 3 into n² − 3 to work out the first three terms of the sequence.

  1. 1n = 1: 1² − 3 = −2
  2. 2n = 2: 2² − 3 = 1
  3. 3n = 3: 3² − 3 = 6
  4. 4First three terms: −2, 1, 6

Answer−2 1 6

Part (b) · 2 marks

Identify the pattern in 1, 3, 9, 27, 81 and write an expression in n for its nth term.

  1. 1Each term is 3 times the one before: 1 = 3⁰, 3 = 3¹, 9 = 3², …
  2. 2nth term = 3ⁿ⁻¹

Answer3ⁿ⁻¹

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