4MA1/1HR Jun 2022, Question 25: 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
Arithmetic series where the sum of 10 terms is 4 times the sum of 5 terms and the 8th term is 45; find the first term, showing algebraic working.
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Solution · 5 marks
- 1S_10 = (10/2)(2a + 9d) = 5(2a + 9d)
- 2S_5 = (5/2)(2a + 4d) = (5/2)(2a + 4d)
- 3S_10 = 4 × S_5 → 5(2a + 9d) = 4 × (5/2)(2a + 4d)
- 45(2a + 9d) = 10(2a + 4d)
- 510a + 45d = 20a + 40d
- 645d − 40d = 20a − 10a
- 75d = 10a
- 8d = 2a
- 98th term: a + 7d = 45
- 10a + 7(2a) = 45
- 11a + 14a = 45
- 1215a = 45
- 13a = 3
Answer3
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