How many multiples of 4 lie between 10 and 250?

Solution:

aₙ = a + (n - 1)d is the n^th term of  an AP.

Here, aₙ is the n^th term, a is the first term, d is the common difference and n is the number of terms.

The first multiple of 4 that is greater than 10 is 12 and the next will be 16.

Therefore, the series will be as follows: 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 which is the largest multiple of 4 within 250.

Hence, the final sequence is as follows: 12, 16, 20, 24, ..., 248

Let 248 be the n^th term of this A.P.

To find the n^th term of the AP , we will use the formula aₙ = a + (n - 1)d,

where a = 12, d = 4, aₙ = 248

248 = 12 + (n - 1)4

236/4 = n - 1

n = 60

There are 60 multiples of 4 between 10 and 250.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 5

Video Solution:

How many multiples of 4 lie between 10 and 250?

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 14

Summary:

The number of multiples of 4 that lie between 10 and 250 is 60.

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