A body starts from rest with uniform acceleration. Its velocity after 2n second is ${\upsilon }_0.$ The displacement of the body in last n seconds is: 

Let $a$ be the acceleration
 
At t = 2n
$v_0=0+a\times 2n=2na$ ………………. (i)
At t = n
$v=an$ 
Between t = n and t = 2n
$v_0^2-v^2=2as$ 
$\Rightarrow 4n^2{a}^2-a^2{n}^2=2as$ 
$\Rightarrow s=\frac{3n^{2}a}{2}$ 
$fromeq.\left(i\right)a=\frac{v_0}{\left(2n\right)}$ 
So,  $s=\frac{3n^2}{2}\left(\frac{v_0}{2n}\right)=\frac{3v_{0}n}{4}$