Haryana Police Constable Model Paper 6

Given:
Geometric progression whose first term is 64 and common multiple is $\frac{1}{2}$
Formula used:
${\mathrm{n}}^{\mathrm{th}}$ term of geometric progression $\left(\mathrm{G}.\mathrm{P}.\right)=\mathrm{a}\times {\mathrm{r}}^{\mathrm{n}-1}$ , where a = first term and r = common multiple
Calculation:
$\mathrm{a}=64,\mathrm{r}=\frac{1}{2}$
$4^{\mathrm{th}}\mathrm{term}=64\times {\left[\frac{1}{2}\right]}^{4-1}$
$\Rightarrow 64\times {\left[\frac{1}{2}\right]}^3$
$\Rightarrow 64\times \frac{1}{8}$
$\Rightarrow 8$
∴ the $4^{\mathrm{th}}$ term in progression is 8