Find the sum of all odd positive integers less than 450.

Find the sum of all odd positive integers less than 450.

Solution :

By wring the odd positive numbers less than 450, we get 

1, 3, 5, 7, ...........447,449

1 + 3 + 5 + 7 +............. + 447 + 449

a = 1, d = 3 - 1  = 2, l = 449

Sn  = (n/2)[a + l]

n = [(l - a)/d] + 1

n = [(449 - 1)/2] + 1

 =  (448/2) + 1

n  = 225

Sn  = (225/2)[1 + 449]

=  (225/2) 450

S225  =  50625