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0606/11 Oct/Nov 2025, Question 5: Geometric Progressions and Sum to Infinity

Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

Arithmetic progression with first term 3 and a sum condition linking the first 10 and first 5 terms; find the common difference, then use linked AP and GP terms to find the GP common ratio r.

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Part (a) · 3 marks

First term 3; sum of first 10 terms is 4 times sum of first 5 terms. Find the common difference.

  1. 1S₁₀ = (10/2)(6 + 9d), S₅ = (5/2)(6 + 4d)
  2. 2(10/2)(6 + 9d) = 4 × (5/2)(6 + 4d)
  3. 330 + 45d = 60 + 40d
  4. 4d = 6

Answerd = 6

Part (b) · 4 marks

1st, 2nd and 5th AP terms are the 1st, 2nd and 3rd GP terms; first terms nonzero. Find r, r ≠ 1.

  1. 1ar = a + d and ar² = a + 4d
  2. 2Eliminate d: ar² = a + 4(ar − a)
  3. 3Divide by a: r² − 4r + 3 = 0
  4. 4(r − 3)(r − 1) = 0
  5. 5r ≠ 1, so r = 3

Answerr = 3

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Also searched as: 0606/11/O/N/25 · 0606_w25_qp_11 · 0606 w25 11 · question 5.
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