4MA1/1H Jan 2021, Question 24: Sum of an Arithmetic Series
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks
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The question, in short
Given an arithmetic series with first term a and common difference d, where the sum of 2n terms equals four times the sum of n terms, express a using d and show the method.
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Solution · 4 marks
- 1Sₙ = (n/2)(2a + (n − 1)d) and S₂ₙ = n(2a + (2n − 1)d)
- 2S₂ₙ = 4Sₙ gives n(2a + (2n − 1)d) = 2n(2a + (n − 1)d)
- 3Divide by n: 2a + 2nd − d = 4a + 2nd − 2d
- 4So 2a − d = 4a − 2d, giving d = 2a
- 5a = d/2
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