Question

The sum of the numbers between $100$ and $1000$ which is divisible by $9$ will be.

• A. $55350$
• B. $57228$
• C. $97015$
• D. $62140$

Answer 1

The correct option is A $55350$

The series start with $108$ which is divisible by $9$ & series end with $999$ which is also divisible by $9$.

Now, series: $108,117,126,....,999$

Series contain $100$ terms as it start from $(12\times 9)$ to $(111\times 9)$. So between $(111$ to $12)$ i.e., $100$ elements are multiplying with $9$ and in between $100$ to $1000$.

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$n=100,a=108,d=117-108=9$

$S_n=\frac{\left(100\right)}{2}\left[2\right(108)+(100-1\left)9\right]$

$=50(216+891)$

$S_n=50\left(1107\right)$

$S_n=55350$.