Let S=1+3+5+.......to n terms. Common difference =2,so the nth term=1+(n-1)*2=2n-1 S=1+3+5+......+(2n-5)+(2n-3)+(2n-1) writing in reverse order S=(2n-1)+(2n-3)+(2n-5)+.......5+3+1 Adding the two series 2S=2n+2n+2n+..........to n terms=2n.2 Therefore S=n^2