Question

The sum of all natural numbers between 250 and 1000 which are exactly divisible by 3 is ____.

Answer 1

The sum of all natural numbers between 250 and 1000 which are exactly divisible by 3 = 252+255+258+ ...................... + 999
                     = 3 (84+85+86+..........................+333)
                     = 3 { (the sum of natural numbers from 1 to 333)  -
                              (the sum of natural numbers from 1 to 83) }
                   = 3 {(333 x 334) /2   - (83 x 84 ) / 2)}(using formula n x n+1)/2 )
                    = 3 ( 55611  - 3486)
                    = 3 x 52125
                    = 156375