4MA1/2HR Jan 2019, Question 23: Sum of an Arithmetic Series
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Given an arithmetic series with 10th term 66 and sum of first 20 terms 1290, find its 5th term, showing working.
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Solution · 4 marks
- 1The 10th term gives a + 9d = 66
- 2The sum of 20 terms gives 10(2a + 19d) = 1290, so 2a + 19d = 129
- 3Substitute a = 66 − 9d: 132 − 18d + 19d = 129
- 4132 + d = 129, so d = −3
- 5a = 66 − 9 × (−3) = 66 + 27 = 93
- 65th term = a + 4d = 93 + 4 × (−3) = 93 − 12 = 81
Answer81
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