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4PM1/02R Jun 2025, Question 4: Geometric Progressions and Sum to Infinity

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 11 marks

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The question, in short

Evaluate a sum of 3(2)^(k−1) from k = 6 to 17, and find the exact sum to infinity of a convergent geometric series G given its third and ninth terms.

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Part (i) · 4 marks

Find the value of the sum from k = 6 to 17 of 3(2)^(k−1).

  1. 1Geometric with a = 3, r = 2
  2. 2Sum of first 17 terms = 3(2¹⁷ − 1) = 393213
  3. 3Sum of first 5 terms = 3(2⁵ − 1) = 93
  4. 4Required sum = 393213 − 93 = 393120

Answer393120

Part (ii) · 7 marks

For geometric series G with positive common ratio, third term 7/13 and ninth term 448/9477, find the exact sum to infinity S.

  1. 1ar² = 7/13 and ar⁸ = 448/9477
  2. 2Divide: r⁶ = (448/9477)/(7/13) = 64/729
  3. 3r = 2/3 (r > 0)
  4. 4a = (7/13)/(4/9) = 63/52
  5. 5S = (63/52)/(1 − 2/3) = 189/52

AnswerS = 189/52

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