Correct option is : (3) 91
\(\mathrm{T}_{2}+\mathrm{T}_{6}=\frac{70}{3}\)
\(\operatorname{ar}+\mathrm{ar}^{5}=\frac{70}{3}\)
\(\mathrm{T}_{3} \cdot \mathrm{T}_{5}=49\)
\(\mathrm{ar}^{2} \cdot \mathrm{ar}^{4}=49\)
\(\mathrm{a}^{2} \mathrm{r}^{6}=49\)
\(\mathrm{ar}^{3}=+7, \mathrm{a}=\frac{7}{\mathrm{r}^{3}}\)
\(\operatorname{ar}\left(1+\mathrm{r}^{4}\right)=\frac{70}{3}\)
\(\frac{7}{\mathrm{r}^{2}}\left(1+\mathrm{r}^{4}\right)=\frac{70}{3}, \mathrm{r}^{2}=\mathrm{t}\)
\(\frac{1}{\mathrm{t}}\left(1+\mathrm{t}^{2}\right)=\frac{10}{3}\)
\(3 \mathrm{t}^{2}-10 \mathrm{t}+3=0\)
\(\mathrm{t}=3, \frac{1}{3}\)
Increasing G.P. \(\mathrm{r}^{2}=3, \mathrm{r}=\sqrt{3}\)
\(\mathrm{T}_{4}+\mathrm{T}_{6}+\mathrm{T}_{8}\)
\(=\mathrm{ar}^{3}+\mathrm{ar}^{5}+\mathrm{ar}^{7}\)
\(=\operatorname{ar}^{3}\left(1+\mathrm{r}^{2}+\mathrm{r}^{4}\right)\)
\(=7(1+3+9)=91\)
