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

Question:

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

Solution:

Numbers between 200 and 500 divisible by 8 are 208, 216, ..., 496.
This forms an AP 208, 216, ..., 496.
So, first term (a) = 208
Common difference (d) = 8

$a_{n}=a+(n-1) d=496$

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

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

$\Rightarrow n-1=36$

$\Rightarrow n=37$

Thus, there are 37 integers between 200 and 500 which are divisible by 8.