Question

find the sum of all 3 digit numbers which when divided by 6 give remainder 4

Answer 1

3 digit numbers are from 100,101..999

Nos divisible by 6 are 102,108,114.....996  

100/6 leaves a reminder 4 so we need to add 2 more to make it 102 which will be divisible by 6

999/6 leaves a reminder 3 so we need to subtract it to make it 996 which will be divisible by 6. note that adding 3 will make it a 4 digit no so we are subtracting.

Since three digit numbers which leave reminder 4 when divided by 6 is asked they will be 102+4,108+4....996+4 ie 106,112....994

a=106 d=6 l=994

an=994=a+(n-1)d

(n-1)6=994-106=888

n-1 = 888/6=148

n=149

Sn=n/2(a+l)=149/2(106+994)=149/2*1100=81950