Question

How many $3-$digit natural numbers are divisible by $7$?

Answer 1

$105,112,......,994$ are in Arthmatic progression

$a=105$

Common difference $=7$

$n^{th}$ term $=a+(n-1)d$

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

$994=105+7n-7$

$994=98+7n$

$994-98=7n$

$7n=896$

$n=\frac{896}{7}$

$n=128$

$\therefore 128$ $3$-digit natural numbers are divisible by $7$.