# Q :  14        Find the sum of the odd numbers between $\small 0$ and $\small 50$.

Odd number between 0 and 50 are
1,3,5,...49
This is an AP with
$here, \ a = 1 \ and \ d = 2$
There are total 25 odd number between 0 and 50
Now, we know that
$S_n= \frac{n}{2}\left \{ 2a+(n-1)d \right \}$
$\Rightarrow S_{25}= \frac{25}{2}\left \{ 2\times 1+(25-1)2 \right \}$
$\Rightarrow S_{25}= \frac{25}{2}\left \{ 2+48 \right \}$
$\Rightarrow S_{25}= \frac{25}{2}\times 50$
$\Rightarrow S_{25}= 25 \times 25 = 625$
Therefore,  sum of the odd numbers between $\small 0$ and $\small 50$  625

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