How many multiples of 4 lie between 10 and 250?

Multiples of 4 between 10 and 250 are :

12, 16, …….., 248.

The above list is an A.P. with first term (a) = 12 and common difference (d) = 16 - 12 = 4.

Given,

Last term of A.P. = 248.

Let nth term be the last term i.e., 248.

∴ a_n = 248

⇒ a + (n - 1)d = 248

⇒ 12 + 4(n - 1) = 248

⇒ 12 + 4n - 4 = 248

⇒ 4n + 8 = 248

⇒ 4n = 240

⇒ n = $\dfrac{240}{4}$ = 60.

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