4MA1/1H Jan 2019, Question 21: Linear Sequences and Common Difference
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks
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The question, in short
Three consecutive terms of an arithmetic sequence are given as (2x + 23), (8x + 2) and (20x − 52). Show that the common difference equals 12.
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Solution · 4 marks
- 1Differences: (8x + 2) − (2x + 23) = 6x − 21 and (20x − 52) − (8x + 2) = 12x − 54
- 2The differences are equal: 6x − 21 = 12x − 54, so 6x = 33 and x = 5.5
- 3Terms: 2 × 5.5 + 23 = 34, 8 × 5.5 + 2 = 46, 20 × 5.5 − 52 = 58
- 446 − 34 = 12 and 58 − 46 = 12, so the common difference is 12
Answer12
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