Question

Find the sum of all $3$ digit no. which when divided by $6$ leaves the remainder $4$.

Answer 1

Let m be the number when divided by $6$ leaves a remainder of $4$

$m=6n+4$

First 3 digit number as such $=100$

Last 3 digit number as such $=994$

$a=100,d=6100+(n-1)6=9946(n-1)=894n=150$

Sum of all numbers $=\frac{150}{2}[200+894]=82050$