Question

Find the number of three digit natural numbers which are divisible by 11

Answer 1

The series of three-digit numbers which are divisible by 11 : $110,121,132,.........990$

The above series is an AP, in which

First term, $a=110$

Common difference, $d=11$

Last term, $L=990$

We know that the $n^{th}$ term of an AP is given by

$a_n=a+(n-1)d$

$\Rightarrow a+(n-1)d=990$ [ Let $n^{th}$ term is $990$]

$\Rightarrow 110+(n-1)\times 11=990$

$\Rightarrow 11\times (n-1)=990-110$

$\Rightarrow 11(n-1)=880$

$\Rightarrow n-1=80$

$\Rightarrow n=81$

Hence, there are 81 three-digit numbers which are divisible by 11.