How many multiples of 4 lie between 10 and 250?

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#### Solution

The 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 the first term as 12 and common difference as 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 n^{th} term of this A.P.

a = 12

d = 4

a_{n} = 248

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

248 = 12 + (n - 1) × 4

248 - 12 = (n - 1) x 4

236 = (n - 1) x 4

`236/4 = n - 1`

59 = n - 1

n = 60

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

Concept: nth Term of an AP

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