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WMA12/01 Jun 2021, Question 1: Arithmetic Progressions in Problems

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Adina's weekly savings start at £5 and rise by £0.25 each week; choose a suitable series model, express week n's amount, and find how many weeks until £350 is reached.

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

Part (ai) · 1 mark

Decide whether the weekly amounts fit an arithmetic or geometric series, giving a reason.

  1. 1Differences: 5.25 − 5 = 0.25 and 5.50 − 5.25 = 0.25
  2. 2Same difference each week, so the series is arithmetic

AnswerArithmetic: the amount goes up by the same £0.25 each week (common difference, no common ratio).

Part (aii) · 2 marks

Give a formula in n for the pounds saved during week n.

  1. 1a = 5, d = 0.25
  2. 2uₙ = a + (n − 1)d
  3. 3uₙ = 5 + 0.25(n − 1) = 4.75 + 0.25n

Answeruₙ = 5 + 0.25(n − 1) (= 4.75 + 0.25n)

Part (b) · 4 marks

With the computer priced at £350, work out how many weeks of saving are needed.

  1. 1Sₙ = n/2 (2×5 + (n − 1)×0.25) ≥ 350
  2. 2n(10 + 0.25n − 0.25) ≥ 700
  3. 30.25n² + 9.75n − 700 ≥ 0, so n² + 39n − 2800 ≥ 0
  4. 4n = (−39 + √(1521 + 11200))/2 = 36.9…
  5. 5So she needs 37 weeks

Answer37 weeks

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