2025 IGCSE Additional Mathematics May/June 0606/12 Q7

2025 IGCSE Additional Mathematics May/June 0606/12 Q7

7 marks

A geometric progression has a 4th term of \(\dfrac{8k^6}{27}\) and a 6th term of \(\dfrac{32k^{10}}{243}\), where \(k\) is a constant.

The common ratio of this geometric progression is positive.

  1. Find the common ratio in terms of \(k\) and the value of the first term of this geometric progression.[4]
  2. Given that this geometric progression has a sum to infinity of \(3\), find the possible values of \(k\).[3]

Solution:

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Answer:(a) Common ratio \(\dfrac{2k^2}3\), first term \(1\). (b) \(k=\pm1\)

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