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

Natural numbers between 200 and 400 which are divisible by 7 are 203, 210, 217, …, 399.

Sum of these numbers forms an arithmetic series 203 + 210 + 217 + … + 399.

Here, first term = a = 203

Common difference = d = 7

∴ a_n = a + (n - 1)d

⇒ 399 = 203 + (n - 1)7

⇒ 399 = 7n + 196

⇒ 7n = 203

⇒ n = 29

∴ there are 29 terms in the AP.

Sum of n terms of this arithmetic series is given by:

S_n = [2a + (n - 1)d]

Therefore sum of 28 terms of this arithmetic series is given by:

∴ S₂₉ = [2(203) + (29 - 1)(7)]

= (29/2) [406 + 196]

=(29/2) × 502

= 7279