Question

How many two-digit numbers are divisible by $5$ ?

Answer 1

Step $1$ : Identify the pattern.

Two-digit numbers divisible by $5$ are $10,15,20,\dots 95.$

This is an A.P. with $a=10$, $a_n=95$ and common difference $d=5$.

Step $2$ : Find the total number of terms in A.P.

We know that, n^th term of an A.P. is given by :

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

$$\begin{gathered} \Rightarrow 95=10+(n-1)5 \\ \Rightarrow 85=(n-1)5 \\ \Rightarrow 17=n-1 \\ \Rightarrow n=18 \end{gathered}$$

Hence, $18$ two-digit numbers are divisible by $5$.