Find the sum of all odd natural numbers less than 50.

Odd numbers less than 50 = 1, 3, 5, ………, 49.

The above series is an A.P. with a = 1, d = 2 and l = 49.

Let there be n terms in series,

⇒ a_n = 49

⇒ a + (n - 1)d = 49

⇒ 1 + 2(n - 1) = 49

⇒ 1 + 2n - 2 = 49

⇒ 2n - 1 = 49

⇒ 2n = 50

⇒ n = 25.

We know that,

$S = \dfrac{n}{2}(a + l) \\[1em] = \dfrac{25}{2}(1 + 49) \\[1em] = \dfrac{25}{2} \times 50 \\[1em] = 625.$

Hence, sum of odd natural numbers less than 50 = 625.