0606/12 Oct/Nov 2025, Question 3: Geometric Progressions and Sum to Infinity
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
A geometric progression has first two terms adding to 9 and a total to infinity of 25. Determine the feasible common ratios and the matching first terms.
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Part (a) · 4 marks
Work out every value the common ratio could take, given the two stated sums.
- 1a + ar = 9
- 2a/(1 − r) = 25 ⇒ a = 25(1 − r)
- 325(1 − r)(1 + r) = 9 ⇒ 1 − r² = 9/25
- 4r² = 16/25 ⇒ r = ±4/5
Answerr = ±4/5
Part (b) · 2 marks
For each common ratio found, calculate the corresponding first term.
- 1a = 25(1 − r)
- 2r = 4/5: a = 25 × 1/5 = 5
- 3r = −4/5: a = 25 × 9/5 = 45
Answerr = 4/5: a = 5; r = −4/5: a = 45
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Also searched as: 0606/12/O/N/25 · 0606_w25_qp_12 · 0606 w25 12 · question 3.
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