4MA1/2H Jun 2018, Question 23: 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
An arithmetic series has its first 48 terms summing to 4 times the first 36 terms; find the sum of the first 30 terms.
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Solution · 5 marks
- 148/2 * (2a + (48 − 1)d) = 4 * (36/2 * (2a + (36 − 1)d))
- 224*(2a + 47d) = 4 * (18*(2a + 35d))
- 324*(2a + 47d) = 72*(2a + 35d)
- 448a + 1128d = 144a + 2520d
- 548a − 144a + 1128d − 2520d = 0
- 6−96a − 1392d = 0
- 796a + 1392d = 0
- 8Divide by 48: 2a + 29d = 0
- 9Now find sum of first 30 terms: 30/2 * (2a + (30 − 1)d)
- 1015*(2a + 29d)
- 11But 2a + 29d = 0, so 15 * 0 = 0
Answer0
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