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WMA12/01 Oct 2024, Question 7: Geometric Progressions and Sum to Infinity

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks

The question, in short

Arithmetic and geometric savings schemes over 300 months: verify a term, total an arithmetic series, then compare totals for two schemes.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Show the month 100 payment for the arithmetic sequence starting at £20 with common difference £0.50.

  1. 1a = 20, d = 0.5
  2. 2u₁₀₀ = a + 99d = 20 + 99 × 0.5
  3. 3= £69.50

AnswerShown: u₁₀₀ = 20 + 99 × 0.5 = £69.50

Part (b) · 2 marks

Find the total paid into scheme A over all 300 months.

  1. 1S₃₀₀ = ½ × 300 × (2 × 20 + 299 × 0.5)
  2. 2= 150 × (40 + 149.5)
  3. 3= £28 425

Answer£28 425

Part (c) · 3 marks

Given £20 in month 1 and £250 in month 300 for the geometric scheme B, find the difference in totals to the nearest £10.

  1. 120r²⁹⁹ = 250, so r = (12.5)^(1/299) = 1.008483…
  2. 2S₃₀₀ = 20(r³⁰⁰ − 1)/(r − 1) = 27 362.95…
  3. 3Difference = 28 425 − 27 362.95 = 1062.05…
  4. 4To the nearest £10: £1060

Answer£1060

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Also searched as: WMA12 October 2024 · WMA12/01 · wma12 oct24 · IAS Maths Pure Mathematics 2 October 2024 · question 7.
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