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.
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