Question

Find how many three digit natural numbers are divisible by 5.

Answer 1

The least positive three digit natural number divisible by 5 is 100.

The sequence divisible by 5 is 100, 105, 110, .... , 995.

Now,
$$\begin{gathered} a_n=a+\left(n-1\right)d \\ \Rightarrow 995=100+\left(n-1\right)\left(5\right) \\ \Rightarrow 995=100+5n-5 \\ \Rightarrow 995=95+5n \\ \Rightarrow 995-95=5n \\ \Rightarrow 5n=900 \\ \Rightarrow n=180 \end{gathered}$$

Hence, 180 three digit natural numbers are divisible by 5.