Question

How many are two-digit numbers divisible by $6$?

Answer 1

Step 1: Establish the AP series

First two-digit number is divisible by $6=12$.

Last two-digit number is divisible by $3=96$.

An arithmetic progression (A.P) is a progression in which the difference between two consecutive terms is constant.

$A.P=12,18,24,30\dots \dots .96$

Here

First-term $\left(a\right)=12$

Common difference $\left(d\right)=6$

Step 2: Calculate the count of numbers

Let us consider there are $n$ numbers then

$a_n=96$

$\Rightarrow$ $a+(n–1)d=96$

$\Rightarrow$$12+(n–1)6=96$

$\Rightarrow$ $12+6n–6=96$

$\Rightarrow$ $6n=90$

$\Rightarrow$ $n=15$

Therefore, two-digit numbers divisible by $6$ is $15$.