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 + (n - 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.