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0606/21 May/Jun 2025, Question 11: Geometric Progressions and Sum to Infinity

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 8 marks

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The question, in short

A geometric progression with r > 0: terms 2 and 3 add to 168 and terms 4 and 5 add to 94.5; find the 6th term and the sum to infinity.

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Part (a) · 7 marks

Form two equations in a and r, divide to find r, then the 6th term.

  1. 1ar + ar² = 168 and ar³ + ar⁴ = 94.5
  2. 2Divide: ar³(1 + r)/(ar(1 + r)) = 94.5/168, so r² = 94.5/168 = 9/16
  3. 3r > 0, so r = 3/4
  4. 4(3/4)a + (9/16)a = 168, so (21/16)a = 168, a = 128
  5. 5u₆ = ar⁵ = 128 × (3/4)⁵ = 243/8

Answer243/8

Part (b) · 1 mark

Sum to infinity using a and r.

  1. 1S∞ = a/(1 − r) = 128/(1 − 3/4)
  2. 2= 512

Answer512

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