4MA1/1HR Jan 2021, Question 21: Sum of an Arithmetic Series
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 6 marks
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The question, in short
An arithmetic series has all positive terms, with u₄ = 6 and S₁₁ = (u₆)² + 18; find u₂₀.
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Solution · 6 marks
- 1u₄ = a + 3d = 6, so a = 6 − 3d
- 2S₁₁ = 11/2 × (2a + 10d) = 11(a + 5d) and u₆ = a + 5d = 6 + 2d
- 3So 11(6 + 2d) = (6 + 2d)² + 18, giving 2d² + d − 6 = 0
- 4(2d − 3)(d + 2) = 0; d = 1.5 since all terms are positive, so a = 1.5
- 5u₂₀ = a + 19d = 1.5 + 28.5 = 30
Answer30
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