Question

Find the sum of all three-digit natural numbers which leave a remainder $2$ when they are divided by $3$.

Answer 1

$104,107,...,998998=104+(n-1)\times 3\Rightarrow \frac{894}{3}=n\cdot 1\Rightarrow n=298+1=299$

Sum $=\frac{299}{2}(104+998)$

$=164749.$