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4PM1/01 Jan 2022, Question 3: Geometric Progressions and Sum to Infinity

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 7 marks

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The question, in short

A geometric series has second term 5/16 and fifth term 135/1024. Find the common ratio and first term, then the sum to infinity given convergence.

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

Part (a) · 5 marks

Find the common ratio r and the first term a from the given second and fifth terms.

  1. 1ar⁴/ar = r³ = (135/1024) ÷ (5/16)
  2. 2r³ = (135 × 16)/(1024 × 5) = 27/64
  3. 3r = 3/4
  4. 4ar = 5/16, so a = (5/16) ÷ (3/4) = 5/12

Answerr = 3/4, a = 5/12

Part (b) · 2 marks

Using the convergent series, find the exact sum to infinity S.

  1. 1S = a/(1 − r) = (5/12)/(1 − 3/4)
  2. 2= (5/12)/(1/4) = 5/3

AnswerS = 5/3

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