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4MA1/2HR Jun 2023, Question 23: Sum of an Arithmetic Series

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks

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The question, in short

An arithmetic sequence starts 8p, 7p − 3, 4p + 2 and its first n terms sum to −1914. Find n, showing working.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Solution · 5 marks

  1. 1(7p − 3) − 8p = (4p + 2) − (7p − 3)
  2. 2−p − 3 = −3p + 5
  3. 32p = 8
  4. 4p = 4
  5. 5a = 8p = 8 × 4 = 32
  6. 6d = (7p − 3) − 8p = −p − 3 = −4 − 3 = −7
  7. 7S_n = n/2 [2×32 + (n − 1)(−7)] = −1914
  8. 8n/2 [64 − 7(n − 1)] = −1914
  9. 9n/2 [64 − 7n + 7] = −1914
  10. 10n/2 [71 − 7n] = −1914
  11. 11n(71 − 7n) = −3828
  12. 1271n − 7n² = −3828
  13. 13−7n² + 71n + 3828 = 0
  14. 147n² − 71n − 3828 = 0
  15. 15(n − 29)(7n + 132) = 0
  16. 16n = 29 or n = −132/7
  17. 17n = 29

Answer29

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