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

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How many multiples of 4 lie between 10 and 250?

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Solution:

We know that 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 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 nth term of this A.P.
a = 12
d = 4
an = 248
an = a + (n - 1) d
248 = 12 + (n - 1) × 4
236/4 = n - 1
59  = n - 1
n = 60
Therefore, there are 60 multiples of 4 between 10 and 250.
Second Method
Multiples of 4 lies between 10 and 250 are 12, 16, 20, ...., 248.
These numbers form an AP with a = 12 and d = 4.
Let number of three-digit numbers divisible by 4 be nan = 248
⇒ a + (n - 1) d = 248
⇒ 12 + (n - 1) × 4 = 248
⇒4(n - 1) = 248
⇒ n - 1 = 59
⇒ n = 60

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by (48.2k points)

Clearly, the numbers between 10 and 250 which are multiple of 4 are 12,16,20,...,248.
This is an AP with first term a=12, common difference d=4.
Let there be n terms in this AP, then
an =248

⇒a+(n−1)d=248

⇒12+(n−1)×4=248

⇒(n−1)=59

⇒n=60