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4MA1/1HR Jun 2020, Question 18: Sum of an Arithmetic Series

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks

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The question, in short

Given an arithmetic sequence with 6th term 39 and 19th term 7.8, calculate the total of its first 25 terms.

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Solution · 4 marks

  1. 1a + 5d = 39
  2. 2a + 18d = 7.8
  3. 3Subtract the first equation from the second: (a + 18d) − (a + 5d) = 7.8 − 39
  4. 413d = −31.2
  5. 5d = −31.2 / 13 = −2.4
  6. 6Substitute d = −2.4 into a + 5d = 39: a + 5(−2.4) = 39
  7. 7a − 12 = 39
  8. 8a = 51
  9. 9Use the sum formula: S_n = n/2 [2a + (n-1)d]
  10. 10S_25 = 25/2 [2(51) + (25-1)(−2.4)]
  11. 11S_25 = 12.5 [102 + 24(−2.4)]
  12. 12S_25 = 12.5 [102 − 57.6]
  13. 13S_25 = 12.5 [44.4]
  14. 14S_25 = 555

Answer555

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