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

First let’s find the numbers between 200 and 400 which are divisible by 7.

The numbers are:

203, 210, 217, … 399

Here, the first term, a = 203

Last term, l = 399 and

Common difference, d = 7

Let’s consider the number of terms of the A.P. to be n.

Hence, a_n = 399 = a + (n –1) d

399 = 203 + (n –1) 7

7 (n –1) = 196

n –1 = 28

n = 29

Then, the sum of 29 terms of the A.P is given by:

\( s_n=\dfrac{29}{2}(203+399)\)

= \(\dfrac{29}{2}(602)\)

= (29)(301)

= 8729

Therefore, the required sum is 8729.