A car starts from rest and moves with a constant acceleration. The ratio of

the distances covered in first n seconds and nth second is

$\text{a}={\text{a m/s}}^2$

distance covered in first n - seconds

$\text{s}=\text{ut}+\frac{1}{2}{\text{at}}^2$

$\text{s}=\frac{1}{2}{\text{an}}^2\cdots \cdots \left(1\right)$

distance covered in ${\text{n}}^{\text{th}}$ second

$\text{s}=\text{u}+\text{a}\left(\text{n}-\frac{1}{2}\right)$

$\text{s}=\text{a}\left(\text{n}-\frac{1}{2}\right)\cdots \cdots \left(2\right)$

$\frac{\left(1\right)}{\left(2\right)}$ we have

$=\frac{\frac{1}{2}{\text{an}}^{\text{2}}}{\frac{\text{a}}{\text{2}}\left(2\text{n}-1\right)}$

${\text{n}}^{\text{2}}:2\text{n}-1$