Question

Find the sum of all three digit natural numbers that are not exactly divisible by 3

Answer 1

i) Sum of all 3 digit natural numbers from 100 to 999 is:
= (900/2)(100 + 999) = 494550 --- (1)
[All these numbers are in AP, with 1st term = 100 and last term = 999; there are 900 terms.
Sum to n terms of an AP = (n/2)(1st + Last)]

ii) 3 digit natural numbers which are divisible by 3 are:
102, 105, 108, 111, ....... 999
This is also in AP, with 1st term = 102 and last term = 999
To find number of terms: a + (n -1)d = last term
102 + (n - 1)*3 = 999; solving n = 300 terms

Thus its sum = (300/2)(102 + 999) = 150 * 1011 = 165150 ----- (2)

iii) So sum of all 3 digit natural numbers, which are not divisible by 3 = (1) - (2)
494550 - 165150 = 329400
hope it's halp