Question

Find the sum of all three-digit numbers which leave a remainder $2$, when divided by $6$.

• A. $82656$
• B. $82658$
• C. $82650$
• D. $82654$

Answer 1

Answer: (C)

$82650$

All three-digit numbers and lying between $100$ and $999$ which leave a remainder of $2$ when divided by $6$.

$104,110,116,..........,998$

As we know nth term, $a_n=a+(n-1)d$

& Sum of first $n$ terms, $S_n=\frac{n}{2}(2a+(n-1\left)d\right)$, where $a$ & $d$ are the first term & common difference of an AP.

$\therefore 998=104+(n-1)\times 6$

$n=150$

Now, $S_{150}=\frac{150}{2}[2\times 104+(150-1)\times 6]$

$=75(208+894)$

$=82650$

Hence, this is the answer.