Find the number of numbers which are divisible by $7$ between $100$ and $1000$.

Given: Numbers from $100$ to $1000$.

To do: To find the number of numbers which are divisible by $7$ between $100$ and $1000$.

The numbers between $100$ and $1000$  that are divisible by $7$  are,

$105,\ 112,\ 119,\ ............,994$ which form an A.P

Here we have:

First term $a=105$

Common difference $d=7$

Last term $a_n=994$

I.e., $a+(n−1)d=994$

$\Rightarrow 105+( n−1)( 7)=994$

$\Rightarrow 7( n−1)=994−105=889$

$\Rightarrow n−1=\frac{889}{7}=127$

$\therefore n=128$

$\therefore$ There are $128$ numbers are there between $100$  $1000$ which are divisible by $7$.