The sum of the first three terms of a G.P.

Let three terms of G.P. are $\frac{\mathrm{a}}{\mathrm{r}}, \mathrm{a}$, ar

product $=27$

$\Rightarrow a^{3}=27 \Rightarrow a=3$

$\mathrm{S}=\frac{3}{\mathrm{r}}+3 \mathrm{r}+3$

For $r>0$

$\frac{\frac{3}{r}+3 r}{2} \geq \sqrt{3^{2}} \quad($ By $\mathrm{AM} \geq \mathrm{GM})$

$\Rightarrow \frac{3}{r}+3 r \geq 6$........(1)

For $r<0 \quad \frac{3}{r}+3 r \leq-6$ $\ldots(2)$

From (1) & (2)

$S \in(-\infty-3] \cup[9, \infty]$