Lemmara logoLemmaraWorked solution

WMA12/01 Oct 2020, Question 8: Geometric Progressions and Sum to Infinity

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 8 marks

The question, in short

Show the geometric sum formula for n terms, then use given second and fifth terms to find the common ratio and the sum of 13 terms.

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

Part (a) · 3 marks

Show that the sum of n terms of a geometric series with first term a and ratio r equals a(1 − rⁿ)/(1 − r).

  1. 1Sₙ = a + ar + ar² + … + arⁿ⁻¹
  2. 2rSₙ = ar + ar² + … + arⁿ⁻¹ + arⁿ
  3. 3Subtract: Sₙ − rSₙ = a − arⁿ
  4. 4(1 − r)Sₙ = a(1 − rⁿ), so Sₙ = a(1 − rⁿ)/(1 − r)

AnswerShown: Sₙ − rSₙ = a − arⁿ, so (1 − r)Sₙ = a(1 − rⁿ) and Sₙ = a(1 − rⁿ)/(1 − r)

Part (b) · 2 marks

Given second term −320 and fifth term 512/25, find the common ratio r.

  1. 1ar = −320 and ar⁴ = 512/25
  2. 2r³ = (512/25) ÷ (−320) = −0.064
  3. 3r = ∛(−0.064) = −0.4

Answerr = −0.4

Part (c) · 3 marks

Using the found ratio, calculate the sum of the first 13 terms to 2 decimal places.

  1. 1a = −320 ÷ (−0.4) = 800
  2. 2S₁₃ = 800(1 − (−0.4)¹³)/(1 − (−0.4))
  3. 3= 800(1 + 0.4¹³)/1.4
  4. 4= 571.43 (2 d.p.)

Answer571.43

Stuck on a step? Read the free lesson: Geometric Progressions and Sum to Infinity

Practise more geometric progressions and sum to infinity questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on geometric progressions and sum to infinity

Also searched as: WMA12 October 2020 · WMA12/01 · wma12 oct20 · IAS Maths Pure Mathematics 2 October 2020 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.