Question

How many multiples of 4 lie between 10 and 250?

Answer 1

First multiple of $4$ that is greater than $10$ is $12$. Next will be $16$.
Therefore, $12, 16, 20, 24, ….$
All these are divisible by $4$ and thus, all these are terms of an A.P. with first term as $12$ and common difference is $4$.
When we divide $250$ by $4$, the remainder will be $2$.
Therefore, $250 − 2 = 248$ is divisible by $4$.
The series is as follows.
$12, 16, 20, 24, …, 248$
Let $248$ be the nth term of this A.P.
$a = 12$
$d = 4$
$a_n = 248$
$a_n = a + (n-1)d$
$248 = 12 + (n-1)4$
$\frac {236}{4} = n-1$
$59 = n-1$
$n = 60$

Therefore, there are $60$ multiples of $4$ between $10$ and $250$.