Question

The sum of all the numbers between 200 and 400 which are divisible by 7 is?

Answer 1

The numbers lying between 200 and 400, which are divisible by 7, are
203, 210, 217,...399
$\therefore$ First term, a=203
Last term, l=399
Common difference, d = 7
Let the number of terms of the A.P be n.
$\therefore a_n=399=a+(n-1)d\Rightarrow 399=203+(n-1)7\Rightarrow 7(n-1)=196\Rightarrow n-1=28\Rightarrow n=29\therefore S_{29}=\frac{29}{2}(203+399)$
$=\frac{29}{2}\left(602\right)$
$=\left(29\right)\left(301\right)$
$=8729$.
Thus, the required sum is 8729.