Question

How many three digit natural numbers are divisible by $9$?

Answer 1

The three-digit natural numbers divisible by $9$ are $108,117,126,..,999$.

Clearly, these numbers are in AP.

Here, $a=108$ and $d=117-108=9$

Let this AP contains n terms. Then, $a_n=999$

$108+(n-1)\times 9=999$

$9n+99=999$

$9n=999-99=900$

$n=100$

Hence, there are $100$ three-digit numbers divisible by $9$.