The product of three consecutive terms of a G.P. is 512 if 4 is added to each of the first and the second of these terms, the three terms now form an A.P. then the sum of the original three terms of the given G.P. is

Let the three terms of G.P. be $\frac{\mathrm{a}}{\mathrm{r}},\mathrm{a}$ and ar
$\therefore$ a³ = 512 $\Rightarrow$ a = 8
Add ins 4 to each term, we have $\frac{8}{\mathrm{r}}{\mathrm{t}}_4,12,8\mathrm{r}$ Since these terms are in A.P.
$\begin{array}{l}24=\frac{8}{\mathrm{r}}+4+8\mathrm{r}\Rightarrow 2{\mathrm{r}}^2-5\mathrm{r}+2=0\\ (2\mathrm{r}-1)(\mathrm{r}-2)=0\Rightarrow \mathrm{r}=2,\mathrm{r}=1/2\end{array}$
for r = 2, terms are 4, 8 and 16
for r = 1/2, terms are 16, 8 and 4
So sum of terms is 28.