Lemmara logoLemmaraWorked solution

0606/12 Feb/Mar 2025, Question 8: Geometric Progressions and Sum to Infinity

Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Two progressions both start at 10: a geometric one with positive ratio r and an arithmetic one with negative difference d. Matching second/fourth and third/sixth terms, find r and d, then decide on a sum to infinity.

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

Part (a) · 6 marks

Use the two term-matching conditions to form equations in r and d, then solve for both values.

  1. 110r = 10 + 3d
  2. 210r² = 10 + 5d
  3. 3r = 1 + 3d/10, so 10(1 + 3d/10)² = 10 + 5d
  4. 49d² + 10d = 0 (or 3r² − 5r + 2 = 0)
  5. 5d ≠ 0 (negative), so d = −10/9
  6. 6r = 1 + 3(−10/9)/10 = 2/3

Answerr = 2/3, d = −10/9

Part (b) · 1 mark

Using the value of r found, decide whether the geometric series converges to a finite sum to infinity.

  1. 1A sum to infinity exists when |r| < 1
  2. 2r = 2/3, so |r| < 1
  3. 3The geometric progression has a sum to infinity

AnswerYes: r = 2/3 and |r| < 1, so the geometric progression has a sum to infinity

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

Practise more geometric progressions and sum to infinity questions

Real 0606 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: 0606/12/F/M/25 · 0606_m25_qp_12 · 0606 m25 12 · question 8.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.