4MA1/2H Jan 2022, Question 26: Sum of an Arithmetic Series
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks
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The question, in short
A prime common difference d and first term a define an arithmetic series; given that the sum of m terms is 39 and of 2m terms is 320, determine d and m, showing algebraic working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 5 marks
- 1Sₘ = m/2 (2a + (m − 1)d) = 39, so 2a + (m − 1)d = 78/m
- 2S₂ₘ = 2m/2 (2a + (2m − 1)d) = 320, so 2a + (2m − 1)d = 320/m
- 3Subtract: md = 242/m, so m²d = 242
- 4242 = 2 × 11², and d is prime, so d = 2
- 5m² = 121, so d = 2 and m = 11
Answerd = 2, m = 11
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