If the product of three terms of a G.P is 216 and the sum of their products taken in pairs is 156 then the greatest term is 

$\text{ Let the terms are }\left(\frac{a}{r}\right)\text{,}\left(\mathrm{a}\right),\left(\mathrm{ar}\right)$

$\begin{array}{l}\text{ Given that }\left(\frac{a}{r}\right)\left(\text{ a }\right)\left(ar\right)=216\\ \to \mathrm{a}=6\\ \\ given that \left(\frac{a}{r}\cdot a\right)+(\underset{ }{\underset{ }{a}\left)\right(ar)}+(\mathrm{ar}\cdot a/r)=156\\ \end{array}$

$$\begin{gathered} \begin{array}{r}\to a^2\left(\frac{1}{r}+r+1\right)=156 \sin ce a=6\\ \Rightarrow 3r^2-10r+3=0\to r=3 or 1/3\end{array} \\ \begin{array}{l}\therefore \text{ the terms are }2,6,18\\ \therefore \text{ the greatest term is }18\end{array} \end{gathered}$$