4MA1/1H Jun 2023, Question 20: Sum of an Arithmetic Series
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks
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The question, in short
An arithmetic series has first 80 terms summing to 470 and 75th term 14.5. Find X given the first X terms sum to 171, showing working.
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Solution · 6 marks
- 1S₈₀ = 40(2a + 79d) = 470, so 2a + 79d = 11.75
- 275th term: a + 74d = 14.5, so 2a + 148d = 29
- 3Subtract: 69d = 17.25, so d = 0.25 and a = 14.5 − 18.5 = −4
- 4Sum of X terms: X/2 × (−8 + 0.25(X − 1)) = 171, so X² − 33X − 1368 = 0
- 5(X − 57)(X + 24) = 0, and X must be positive, so X = 57
Answer57
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