Multiples of 4 lie between 10 and 250: 12, 16, 20, …, 248
Let the total number of multiples of 4 lie between 10 and 250 be n.
Here, a = 12 and d = 16 – 12 = 4. To find: n, where a_n = 248.
Given that: a_n = a + (n – 1)d = 248
⇒ 12 + (n -1)(4) = 248 ⇒ 4(n -1) = 236
⇒ n – 1 = 236/4 = 59 ⇒ n = 60
Hence, the total number of multiples of 4 lie between 10 and 250 is 60.