Question

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

Answer 1

1st odd no.=1
last odd no.=49

a=1, an or l=49, common diff. d= 2,

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

=1+(n-1)2=49

=1+2n-2=49

=2n-1=49

=2n=49=1

=2n=50

n=25

$S_n=\frac{n}{2}[a+L]$

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

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

$=25\times 25=625$

therefore sum of all odd integers between 0 to 50 is 625