Question

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

Answer 1

The odd numbers between 0 and 50 are
$1, 3, 5, 7, 9 …. \ 49$
Therefore, it can be observed that these odd numbers are in an A.P.
$a = 1$, $d = 2$ and $l = 49$
$l = a + (n − 1) d$
$49 = 1 + (n − 1)2$
$48 = 2(n − 1)$
$n − 1 = 24$
$n = 25$
$S_n = \frac {n}{2} [a+l]$

$S_{25} = \frac {25}{2} [1+49]$

$S_{25} = \frac {25\times50}{2}$
$S_{25} = 25\times25$
$S_{25} = 625$