4MA1/1HR Jun 2024, Question 23: 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
Three consecutive terms of an arithmetic sequence are given in x. Determine the total of the first 40 terms as an integer, showing full algebraic working.
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Solution · 4 marks
- 1Equal differences: (7x − 9) − (x + 2) = (x + 2) − (4x − 14)
- 26x − 11 = 16 − 3x, so 9x = 27 and x = 3
- 3Terms are −2, 5, 12, so a = −2 and d = 7
- 4S₄₀ = 40/2 × (2 × (−2) + 39 × 7) = 20 × 269 = 5380
Answer5380
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