Question

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

Answer 1

The odd numbers between $0$ and $50$ are $1,3,5,7,9\dots 49$
Therefore, it can be observed that these odd numbers are in an A.P.

$a=1,d=2,l=49$

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

$49=1+(n-1)2$

$48=2(n-1)$

$n-1=24$

$n=25$

$S_n=\frac{n}{2}(a+l)$

$S_{25}=\frac{25}{2}(1+49)$

$=\frac{25\times 50}{2}=625$