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0580/22 Feb/Mar 2021, Question 14: Linear Sequences and Common Difference

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

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The question, in short

Two sequences are given: find the next two terms of 29, 22, 15, 8, and find the nth term of 4, 7, 12, 19, 28.

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Part (a) · 2 marks

Write down the next two terms of the sequence 29, 22, 15, 8.

  1. 1Term-to-term rule: subtract 7
  2. 28 − 7 = 1, 1 − 7 = −6
  3. 3Next two terms: 1, −6

Answer1 −6

Part (b) · 2 marks

Find the nth term of the sequence 4, 7, 12, 19, 28.

  1. 1First differences: 3, 5, 7, 9; second differences: 2
  2. 2So the sequence is based on n²: 1, 4, 9, 16, 25
  3. 3Each term is 3 more than n²
  4. 4nth term = n² + 3

Answern² + 3

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Also searched as: 0580/22/F/M/21 · 0580_m21_qp_22 · 0580 m21 22 · question 14.
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