Question

Find the sum of all three digit numbers which are multiplies of 9

Answer 1

First three digit number divisible by 9 is 108.

⇒ a = 108

⇒ d = 9

⇒ n = ?

⇒ L = 999

Applying the formula: L = a + ( n - 1 ) d , we get,

⇒ 999 = 108 + ( n - 1 ) 9

⇒ 999 - 108 = ( n - 1 ) 9

⇒ 891 = ( n - 1 ) 9

⇒ 891 / 9 = ( n - 1 )

⇒ 99 = ( n - 1 )

⇒ 99 + 1 = n

⇒ 100 = n

Hence the sum of all three digit natural numbers which are a multiple of 9 is 55,350.