Question

How many multiples of $4$ lie between $10$ and $250$$?$

Answer 1

Step $1:$ Obtain an arithmetic progression.

Since, the first and last number which are the multiple of $4$ and lies between $10$ and $205$ are $12$ and $248$ respectively.

We know that the multiple of $4$ occurs after $4$ numbers.

So, the arithmetic progression is $12,16,20,......248$.

Step $2:$ Find the number of terms in the arithmetic progression.

The formula of $n^{th}$ term of an A.P is $a_n=a+(n-1)d$.

Since, $a=12$ and $d=4$.

Find the number of terms as follows:

$$\begin{gathered} 248=12+(n-1)4 \\ \Rightarrow 248=12+4n-4 \\ \Rightarrow 248=8+4n \\ \Rightarrow 240=4n \end{gathered}$$

Therefore, the value of $n$ is $60$.

Hence, $60$ multiples of $4$ lie between $10$ and $250$.