Question

Find how many three digits natural numbers are divisible by $5$.

Answer 1

Three digit number are $100,\mathrm{105.........995}$

a$=100$ (a= first term)

d$=105-100=5$ (d=common difference)

$\begin{array}{c}\Rightarrow a_n=a+(n-1)d\\ \Rightarrow 995=100+(n-1)5\\ \Rightarrow 995-100=(n-1)5\\ \Rightarrow \frac{895}{5}=n-1\\ \Rightarrow 179=n-1\\ \Rightarrow n=179+1\\ \Rightarrow n=180\end{array}$

Hence,

$180$ three digit natural number are divisible by 5.