Common ratio of a positive geometric progression and a later term in standard form

Common ratio of a positive geometric progression and a later term in standard form

IB Year 6 | Grade 12
6 marks

Every term of the geometric progression \(u_1, u_2, u_3, \ldots\) is positive. The fourth term is \(2.7\times10^4\) and the sixth term is \(2.43\times10^5\).

  1. Find the common ratio of the progression.[3]
  2. Find \(u_{10}\), giving your answer in the form \(a\times10^k\), where \(1\leq a<10\) and \(k\in\mathbb{Z}\).[3]

Solution:

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Answer:(a) \(r=3\) (b) \(u_{10}=1.9683\times10^7\)

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