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0580/32 May/Jun 2025, Question 13: Linear Sequences and Common Difference

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 5 marks

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The question, in short

A sequence starts at 2 and reaches 20 as its fourth term by repeatedly adding k; determine e, f and k, then find the nth term of 9, 7, 5, 3.

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Part (a) · 3 marks

Using a first term of 2 and fourth term of 20 with a constant addition k, work out the missing terms e and f and the value of k.

  1. 1From 1st term to 4th term is 3 steps: 3k = 20 − 2 = 18
  2. 2k = 6
  3. 3e = 2 + 6 = 8, f = 8 + 6 = 14
  4. 4e = 8, f = 14, k = 6

Answere = 8, f = 14, k = 6

Part (b) · 2 marks

For the sequence 9, 7, 5, 3, give an expression in n that generates each term.

  1. 1Terms go down by 2, so nth term = −2n + c
  2. 2First term: −2 × 1 + c = 9, so c = 11
  3. 3nth term = 11 − 2n

Answer11 − 2n

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