How many multiples of 4 lie between 10 and 250?

In this problem, we need to find out how many multiples of 4 lie between 10 and 250.

So, we know that the first multiple of 4 after 10 is 12 and the last multiple of 4 before 250 is 248. Also, all the terms which are divisible by 4 will form an A.P. with the common difference of 4.

So here,

First term (a) = 12

Last term (an) = 248

Common difference (d) = 4

So, let us take the number of terms as n

Now, as we know,

$a_{n}=a+(n-1) d$

So, for the last term,

$248=12+(n-1) 4$

$248=12+4 n-4$

$248=8+4 n$

$248-8=4 n$

Further simplifying,

$240=4 n$

$n=\frac{240}{4}$

$n=60$

Therefore, the number of multiples of 4 that lie between 10 and 250 is 60 .