Question

What is the sum of all odd numbers between 500 and 600?

Answer 1

sum of all odd numbers between 500 and 600 will be 27,500

Answer 2

first odd number after 500 is 501 and last odd no. befor 600 is 599
it forms a ap eg.
501,503,505.....

in this AP
odd no between 500 and 600
=(599-501)/2+1
=50

d=503-501=2

n=50


sum of no in ap
=n/2(2a+(n-1)d)


put all the values

=50/2[2(501)+(50-1)2]
=25[1002+(49)2]
=25[1002+98]
=25[1100]
=27,500

so the sum of numbers between 500 and 600 is 27,500.