Find the sum of all odd numbers between 0 and 50.
Question:
Find the sum of all odd numbers between 0 and 50.

Solution:
All odd numbers between 0 and 50 are 1, 3, 5, 7, …, 49.
This is an AP in which a = 1, d = (3 – 1) = 2 and l = 49.

Let the number of terms be n.
Then, Tn = 49
a + (– 1)d = 49
⇒ 1 + (n – 1​) ⨯ 2 = 49
⇒ 2n = 50
⇒ n = 25

$\therefore$ Required sum $=\frac{n}{2}(a+l)$

$=\frac{25}{2}[1+49]=25 \times 25=625$

Hence, the required sum is 625.