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0580/22 Feb/Mar 2022, Question 10: Quadratic and Cubic Sequences

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

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The question, in short

For a sequence with nth term n² + 7, find its first three terms, then work out the nth term rule for a second sequence starting 15, 7, −1, −9.

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Part (a) · 2 marks

Substitute n = 1, 2 and 3 into n² + 7 to find the first three terms.

  1. 1n = 1: 1² + 7 = 8
  2. 2n = 2: 2² + 7 = 11
  3. 3n = 3: 3² + 7 = 16
  4. 4First three terms: 8, 11, 16

Answer8, 11, 16

Part (b) · 2 marks

From the terms 15, 7, −1, −9, determine the nth term of this arithmetic sequence.

  1. 1Common difference = 7 − 15 = −8
  2. 2Term before the first (zero term) = 15 + 8 = 23
  3. 3nth term = 23 − 8n

Answer23 − 8n

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