4PM1/01 Jan 2023, Question 1: Arithmetic Progressions in Problems
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 4 marks
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The question, in short
An arithmetic sequence has terms aₙ with the sum of the 10th, 11th and 12th terms equal to 129, and the sum of the 19th, 20th and 21st terms equal to 237. Determine the first term a₁.
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Solution · 4 marks
- 1a₁₀ + a₁₁ + a₁₂ = 3a₁₁ = 129, so a₁ + 10d = 43
- 2a₁₉ + a₂₀ + a₂₁ = 3a₂₀ = 237, so a₁ + 19d = 79
- 3Subtract: 9d = 36, d = 4
- 4a₁ = 43 − 40 = 3
Answera₁ = 3
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