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0580/12 Oct/Nov 2022, Question 12: Pattern Sequences and Special Sequences

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 4 marks

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The question, in short

Two sequences are given by their first five terms: 27, 26, 23, 18, 11 and 3, 10, 17, 24, 31. Work out the required terms and formula.

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Part (a) · 2 marks

Continue the sequence 27, 26, 23, 18, 11 by working out the two terms that follow.

  1. 1Differences: −1, −3, −5, −7, so next are −9, −11
  2. 211 − 9 = 2, 2 − 11 = −9
  3. 3Next two terms: 2, −9

Answer2, −9

Part (b) · 2 marks

For the sequence 3, 10, 17, 24, 31, work out an expression for the nth term.

  1. 1Difference = 7, so 7n + c
  2. 27 × 1 + c = 3, so c = −4
  3. 3nth term = 7n − 4

Answer7n − 4

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