Question

The sum of the odd numbers between $0$ and $50$ is :

• A. $525$
• B. $625$
• C. $425$
• D. $725$

Answer 1

The correct option is B $625$

Odd numbers between $0$ and $50$ are $1,3,5,7,...........,49$

By using, $a_n=a+(n-1)d$
$\therefore 49=a+(n-1)d$
$\Rightarrow 49=1+(n-1)2$
$\Rightarrow 48=2n-2$
$\Rightarrow 2n=50$
$\Rightarrow n=25$
Now, $S_{25}=\frac{n}{2}(a+1)$
$\Rightarrow S_{25}=\frac{25}{2}(1+49)$
$\Rightarrow \frac{25}{2}\times 50=625$