How many 3 - digit numbers are divisible by 7?

To Find : 3 - digit numbers divisible by 7.

First 3 - digit number divisible by 7 is 105

Second 3 - digit number divisible by 7 is 112 and

Last 3 - digit number divisible by 7 is 994 .

Given: The AP is $105,112,119$, , 994 $a_{1}=105, a_{2}=112, d=112-105=7$ and $a_{n}=994$

(Where $a=a_{1}$ is First term, $a_{2}$ is Second term, $a_{n}$ is nth term and $d$ is common difference of given $\mathrm{AP}$ )

Formula Used: $a_{n}=a+(n-1) d$

$994=105+(n-1) 7$

$889=(n-1) 7$

$127=(n-1)$

$n=128$

So, There are total of 128 three - digit number which is divisible by 7.