Question

Find how many integers between $200$ and $500$ are divisible by $8.$

Answer 1

Numbers between $200$ and $500$ divisible by $8$ are $208,216,...,496.$
This forms an AP $208,216,...,496.$
So, first term $\left(a\right)=208$
Common difference $\left(d\right)=8$
$a_n=a+(n-1)d=496$ [$\because$ last term $=496$]

$\Rightarrow 208+(n-1)8=496$

$\Rightarrow (n-1)8=288$

$\Rightarrow n-1=36$

$\Rightarrow n=37$
Thus, there are $37$ integers between $200$ and $500$ which are divisible by $8.$