# 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.

**☛ Related Questions:**

- For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, ... equal?
- Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12.
- Find the 20th term from the last term of the A.P. 3, 8, 13,..., 253.
- The sum of the 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.

visual curriculum