Question

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

Answer 1

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

This is an AP with a = 203, d = 7 and `l` = 399.

Suppose there are n terms in the AP. Then,

a_n = 399 

⇒ 203 + (n – 1) × 7 = 399   ...[a_n = a + (n – 1)d] 

⇒ 7n + 196 = 399

⇒ 7n = 399 – 196

⇒ 7n = 203

⇒ n = 29 

∴ Required sum = `29/2 (203 + 399)`   ...`[S_n = n/2 (a + l)]`

= `29/2 xx 602`

= 8729

Hence, the required sum is 8729.