Question

The sum of all numbers from 1 to 1000 which are neither divisible by 2 nor by 5 is

Answer 1

Numbers which can divided by 2 = 2,4,6,........1000

an = 1000

a = 2

1000 = 2 + 2n - 2

n = 500

Sum = a x n(n+1)/2   = 500 x 501  = 250500

Numbers which can be divided by 5 = 5, 10, 15, .......1000

1000 = 5 + 5n - 5 = 5n

n = 1000/5 = 200

Sum = 5 x 200 x 201/2 =  100500

Sum of the numbers which can be divisible 2 and 5 ie 10

10, 20, ...... 1000

1000 = 10 + 10n - 10

n = 1000/10 = 100

Sum  = 10 x 100 x 101/ 2  = 50500

Sum of all numbers upto 1000 = 1,2,.......1000

n(n+1)/2   = 1 x 1000 x 1001/2   = 500500

Sum of the numbers from 1 to 1000 which neither divisible by 2 nor 5

= 500500 - (250500 + 100500 + 50500)

= 500500 - 300500 = 200000