Discussion
The three geometric means between 4 and 324 are
Answer: E
The geometric means are 12, 36, 108.
Inserting three geometric means between 4 and 324 makes a G.P. of five terms with first term 4 and fifth term 324.
\[ \begin{aligned} 4r^{4} &= 324 \\ r^{4} &= 81 \Rightarrow r = 3 \end{aligned} \]
So the terms are 4, 12, 36, 108, 324. Each of the other options has one wrong term: 46, 128, 14 and 98 do not continue a common ratio of 3.
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