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WMA12/01 Jan 2022, Question 8: Geometric Sequences in Context

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 9 marks

The question, in short

A post is hammered into soil; successive hit distances start at 100 mm, 98 mm, 96 mm and continue as an arithmetic sequence, then change to a geometric sequence after hit 20. Work out distances, a ratio and a hit count.

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

Part (a) · 1 mark

Confirm that the 20th hit moves the post an extra 62 mm.

  1. 1a = 100, d = −2
  2. 2u₂₀ = 100 + 19 × (−2) = 62 mm

AnswerShown: u₂₀ = 100 + 19(−2) = 62 mm

Part (b) · 2 marks

Calculate the cumulative depth reached after 20 hits.

  1. 1S₂₀ = ½ × 20 × (100 + 62)
  2. 2= 10 × 162 = 1620 mm

Answer1620 mm

Part (c) · 2 marks

Using 60 mm on hit 22, determine the geometric common ratio r to 3 decimal places.

  1. 1The 20th hit (62 mm) starts the GP, so the 22nd hit is 62r²
  2. 262r² = 60, so r² = 60/62
  3. 3r = √(60/62) = 0.98373… = 0.984 (3 d.p.)

Answerr = 0.984

Part (d) · 4 marks

Find the least number of hits N for total depth to exceed 3 m, showing all working.

  1. 1Distance from hits 21 to 20 + n: 62r(1 − rⁿ)/(1 − r), with r = 0.98373…
  2. 21620 + 62r(1 − rⁿ)/(1 − r) > 3000
  3. 31 − rⁿ > 1380(1 − r)/(62r), so rⁿ < 0.63207…
  4. 4n > log(0.63207…)/log(0.98373…) = 27.98…, so n = 28
  5. 5N = 20 + 28 = 48

AnswerN = 48

Stuck on a step? Read the free lesson: Geometric Sequences in Context

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