Find the sum of all 3 digit no.'s not divisible by 9
Answers
no. are
6,12,15,21,24,30,33.....and so on
order by
up vote
2
down vote
accepted
An arithmetic progression is a sequence of number of the form a,a+d,a+2d,a+3d,..,a+nd, that is every two consecutive numbers differ by the same value called d.
The formula for the sum of the first n terms of a progression starting at a with common difference d is n2[2a+(n−1)d].
To solve your problem we need to add all the numbers from 100 to 999 and then subtract the numbers that can be divided exactly by 3.
The sum of the numbers is the sum of the first 900 terms of a progression with a=100 and d=1, that is 9002(200+899)=494550
Now we need to calculate the sum of the first ⌈999−1003⌉=300 terms of the sequence with a=102 and d=2, that is 3002(2(102)+3(299))=165150, the result is then 494550−165150=329400