Question

Find the number of integers between 100 & 1000 that are divisible by 7.

Answer 1

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

$105,112,119,............,994$ which from an A.P with

First term $a=105$

Common difference $d=7$

Last term $a_n=994$

I.e., $a+(n-1)d=994$

$⟹105+(n-1)\left(7\right)=994$

$⟹7(n-1)=994-105=889$

$⟹n-1=\frac{889}{7}=127$

$\therefore n=128$

I.e., there are $128$ numbers are there between $100$ & $1000$ which are divisible by $7$.