Question

Find the sum of all natural numbers between 100 and 500 which are divisible by 7.

Answer 1

All the natural numbers between 100 and 500 which are divisible by 7 are 105, 112, 117, 126,..., 497.

This is an AP in which a = 105, d = (112 - 105) = 7 and l = 497.

Let the number of terms be n.
Then T_n = 497
⇒ a + (n - 1)d = 497
⇒ 105 + (n - 1​) ⨯​ 7 = 497
⇒ 7n = 399
⇒ n = 57

∴ Required sum = $\frac{n}{2}\left(a+l\right)$
= $\frac{57}{2}\left[105+497\right]=57\times 301=17157$
Hence, the required sum is 17157