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WMA12/01 Oct 2020, Question 5: Arithmetic Progressions in Problems

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 11 marks

The question, in short

Ben saves £100 then £5 more each month for 60 months; Lina saves £600 then £10 less each month. Find terms, totals, form and solve an equation in n, and judge a solution.

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

Part (a) · 2 marks

Find how much Ben saves in month 40 of his arithmetic sequence.

  1. 1a = 100, d = 5, n = 40
  2. 2u₄₀ = 100 + 39 × 5 = 295

Answer£295

Part (b) · 3 marks

Find Ben's total savings across all 60 months.

  1. 1S₆₀ = ½ × 60 × (2 × 100 + 59 × 5)
  2. 2= 30 × (200 + 295)
  3. 3= 30 × 495 = 14 850

Answer£14 850

Part (c) · 3 marks

Using Lina's savings reaching £18 200 after n months, form an equation and show it becomes n² − 121n + 3640 = 0.

  1. 1½n(2 × 600 + (n − 1)(−10)) = 18 200
  2. 2½n(1210 − 10n) = 18 200
  3. 3605n − 5n² = 18 200
  4. 45n² − 605n + 18 200 = 0, so n² − 121n + 3640 = 0

AnswerShown: ½n(1200 − 10(n − 1)) = 18 200 simplifies to n² − 121n + 3640 = 0

Part (d) · 2 marks

Solve the quadratic equation n² − 121n + 3640 = 0 for n.

  1. 1n² − 121n + 3640 = 0
  2. 2(n − 56)(n − 65) = 0
  3. 3n = 56 or n = 65

Answern = 56 or n = 65

Part (e) · 1 mark

Say which solution for n is not sensible and give a reason.

  1. 1Term 65 would be 600 + 64 × (−10) = −40, a negative saving
  2. 2So n = 65 is not sensible; she reaches £18 200 at n = 56

Answern = 65, because Lina has already saved £18 200 after 56 months (her 65th month would be a negative amount, 600 − 64 × 10 = −40)

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Also searched as: WMA12 October 2020 · WMA12/01 · wma12 oct20 · IAS Maths Pure Mathematics 2 October 2020 · question 5.
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