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4PM1/01R Jan 2022, Question 2: Arithmetic Progressions in Problems

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 8 marks

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The question, in short

Arithmetic series with nth term uₙ, where u₅ = 46 and u₂₀ = 181. Find the common difference, first term, and the sum of terms from n = 21 to 50.

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Part (a) · 4 marks

Using u₅ = 46 and u₂₀ = 181, find (i) the common difference and (ii) the first term of the series.

  1. 1a + 4d = 46
  2. 2a + 19d = 181
  3. 3Subtract: 15d = 135, d = 9
  4. 4a = 46 − 36 = 10

Answer(i) d = 9 (ii) a = 10

Part (b) · 4 marks

Evaluate the sum of uₙ from n = 21 to 50.

  1. 1S₅₀ = 25(2 × 10 + 49 × 9) = 11525
  2. 2S₂₀ = 10(2 × 10 + 19 × 9) = 1910
  3. 3∑ from 21 to 50 = 11525 − 1910 = 9615

Answer9615

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