Find the sum of all numbers between 200 and 400 which are divisible by 7.

The numbers lying between 200 and 400, which are divisible by 7, are

203, 210, 217, ­­­­­­­­… 399

∴First term, a = 203

Last term, l = 399

Common difference, d = 7

Let the number of terms of the A.P. be n.

$\therefore a_{n}=399=a+(n-1) d$

$\Rightarrow 399=203+(n-1) 7$

$\Rightarrow 7(n-1)=196$

$\Rightarrow n-1=28$

$\Rightarrow n=29$

$\therefore \mathrm{S}_{29}=\frac{29}{2}(203+399)$

$=\frac{29}{2}(602)$

$=(29)(301)$

$=8729$

Thus, the required sum is 8729.