Positive common ratio of a geometric sequence from two terms and its first term in standard form

Positive common ratio of a geometric sequence from two terms and its first term in standard form

6 marks

All the terms of a geometric sequence \(u_1,u_2,u_3,\dots\) are positive, and its common ratio is \(r\). The third term is \(7.2\times10^4\) and the fifth term is \(1.8\times10^4\).

  1. Find the value of \(r\).[3]
  2. Find \(u_1\), expressing it as \(a\times10^k\) with \(1\leq a<10\) and \(k\in\mathbb{Z}\).[3]

Solution:

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Answer:(a) \(r=\dfrac12\) (b) \(u_1=2.88\times10^5\)

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