Question

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

Answer 1

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.

∴ $a_n=a+(n-1)d$ = 399

⇒ 399 = 203 + (n –1) 7

⇒ 7 (n –1) = 196

⇒ n –1 = 28

⇒ n = 29

$S_n=\frac{n}{2}[a+L]$

$S_{29}=\frac{29}{2}[203+399]$

$=\frac{29}{2}\times 602=8729$

Thus, the required sum is 8729.