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

Given:

Odd numbers between 0 and 50.

To do:

We have to find the sum of all odd numbers between 0 and 50.

Solution:

Odd numbers between 0 and 50 are \( 1,3,5,7, \ldots, 49 \).

The sequence is in A.P.

Here,

\( a=1 \) and \( d=3-1=2 \) \( l=49 \)

We know that,

$l=a+(n-1) d$

$\Rightarrow 49=1+(n-1) \times 2$

$\Rightarrow 49=1+2 n-2$

$\Rightarrow 49+1=2 n$

$\Rightarrow n=\frac{50}{2}=25$

$\therefore n=25$

We know that,

$\mathrm{S}_{n}=\frac{n}{2}[2 a+(n-1) d]$

$=\frac{25}{2}[2 \times 1+(25-1) \times 2]$

$=\frac{25}{2}[2+24 \times 2]$

$=\frac{25}{2}(50)$

$=25 \times 25$

$=625$

The sum of all odd numbers between 0 and 50 is $625$.