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

Solution:

The number 12 is the first multiple of four that is greater than ten.

The following multiple will be 16.

As a result, the series formed as follows: 12, 16, 20, 24,…

All of these are divisible by 4, hence they are all terms of an A.P. with 12 as the first term and 4 as the common difference.

The residual is 2 when we divide 250 by 4. As a result, 250 2 = 248 is divisible by four.

The current series is as follows:

12, 16, 20, 24, …, 248

Let the nth term of this A.P. be 248.

The first term, a = 12

The common difference, d = 4

an = 248

As we all know,

an = a+(n−1)d

248 = 12+(n-1)×4

236/4 = n-1

59  = n-1

n = 60

As a result, there are 60 multiples of 4 in the range of 10 to 250.