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4PM1/01 Jun 2020, Question 6: Arithmetic Progressions in Problems

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 10 marks

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The question, in short

Arithmetic series A has sum Sₙ = n(15 + 2n). Find a and d, the 20th term, and the value of p satisfying S₂ₚ − 2Sₚ = 1 + S₍ₚ₋₁₎.

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Part (a) · 4 marks

Use the given sum formula to find the first term a and the common difference d of the series.

  1. 1a = S₁ = 1 × (15 + 2) = 17
  2. 2S₂ = 2(15 + 4) = 38 = 2a + d
  3. 334 + d = 38 ⇒ d = 4

Answera = 17, d = 4

Part (b) · 2 marks

Calculate the 20th term of the arithmetic series A.

  1. 1u₂₀ = a + 19d
  2. 2= 17 + 19 × 4 = 93

Answer93

Part (c) · 4 marks

Given S₂ₚ − 2Sₚ = 1 + S₍ₚ₋₁₎, find the value of p.

  1. 12p(15 + 4p) − 2p(15 + 2p) = 1 + (p − 1)(15 + 2(p − 1))
  2. 24p² = 1 + (p − 1)(13 + 2p)
  3. 32p² − 11p + 12 = 0
  4. 4(2p − 3)(p − 4) = 0
  5. 5p must be an integer, so p = 4

Answerp = 4

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