The next term of the G.P.$\mathrm{x},{\mathrm{x}}^2+2,\text{ and }{\mathrm{x}}^3+10$ is

$\mathrm{x},{\mathrm{x}}^2+2,{\mathrm{x}}^3+10$ are in G.P. Hence,
$\mathrm{x}\left({\mathrm{x}}^3+10\right)={\left({\mathrm{x}}^2+2\right)}^2\Rightarrow x^4+10x={\mathrm{x}}^4+4{\mathrm{x}}^2+4$
$\Rightarrow 4{\mathrm{x}}^2-10\mathrm{x}+4=0$
or $2{\mathrm{x}}^2-5\mathrm{x}+2=0$
or $\mathrm{x}=2,\frac{1}{2}$
The 4th term of G.P. is
$\left({\mathrm{x}}^3+10\right)\mathrm{r}=\left({\mathrm{x}}^3+10\right)\left(\frac{{\mathrm{x}}^2+2}{\mathrm{x}}\right)=\left\{\begin{array}{l}54\text{ when }\mathrm{x}=2\\ \frac{729}{16}\text{ when }\mathrm{x}=\frac{1}{2}\end{array}\right.$