4MA1/1HR Jan 2023, Question 24: Sum of an Arithmetic Series
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
An arithmetic sequence starts at 8 with common difference 11 and has k terms, k > 21. Given the last 20 terms sum to 10170, find k, showing algebraic working.
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Solution · 5 marks
- 1The last 20 terms start at term k − 19, which is 8 + 11(k − 20) = 11k − 212
- 2Sum = 20/2 × [2(11k − 212) + 19 × 11] = 10 170
- 3So 2(11k − 212) + 209 = 1017, giving 22k − 215 = 1017
- 422k = 1232, so k = 56
Answer56
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