4MA1/1HR Jun 2019, Question 19: 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 with 25th term 44.5 and sum of first 30 terms 765; find the 16th term, showing working.
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Solution · 5 marks
- 125th term: a + 24d = 44.5
- 2Sum of 30 terms: 30/2 × (2a + 29d) = 765
- 315(2a + 29d) = 765
- 42a + 29d = 51
- 5Double the first equation: 2a + 48d = 89
- 6Subtract: (2a + 48d) − (2a + 29d) = 89 − 51
- 719d = 38
- 8d = 2
- 9Substitute into a + 24d = 44.5: a + 48 = 44.5
- 10a = −3.5
- 1116th term = a + 15d = −3.5 + 15 × 2
- 12−3.5 + 30 = 26.5
- 13The 16th term is 26.5
Answer26.5
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