Question

How many multiples of 4 lie between 10 and 250?
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Answer 1

How many multiples of 4 lie between 10 and 250?

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The answer is 60.

Method 1: To arrive at the answer, we can either list down all the multiples of 4 between 10 and 250 and count them. This however is a little time consuming. So, lets move onto the other alternatives.

Method 2: First let us find the number of multiples of 4 between 1 and 10 which would be 10/4=2.5

Number of multiples of 4 between 1 and 250 = 250/4=62.5

So, the number of multiples of 4 between 10 and 250 would be

(Number of multiples of 4 between 1 and 250) - (Number of multiples of 4 between 1 and 10)

62.5−2.5=60

Method 3: We need to find the number of multiples of 4 between 10 and 250.

The list of numbers would be as follows:

12,16,20,24,28,32,36,40,........248.

The above list is an arithmetic series/arithmetic progression where the first number is 12, the last number is 248 and the common difference between the numbers is 4.

The nth term in an arithmetic sequence = a + (n-1)*d where a is the first term, d is the common difference.

In the arithmetic series above, a =12, d = 4 and let us assume there are n terms and we need to find the value of n. We know that the value of the last term i.e. nth term is 248.

So, 248=12+(n−1)∗4

248=12+4n−4

248=4n+8

248–8=4n

240=4n

n=240/4=60

Thus, 248 is the 60th term in the series and hence there are 60 terms in the series.

Therefore number of multiples of 4 between 10 and 250 is 60.

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Answer 2

$\bf{\underline{Solution}}:-$

➟ Multiples of 4 lie between 10 and 250 are 12,16,20...........,248.

This is an Arithmetic progression (AP)

Given :-

• First term (a) = 12

• Common difference (d) = 16-12 = 4

• $\rm\:a_n=248$

To find :-

• How many multiples of 4 lies between 10 and 250

Solution :-

We know that,

$\blue{\bigstar}\:\:{\underline{\boxed{\bf\red{a_n=a+(n-1)d}}}}$

⤇ 248 = 12 + (n - 1) × 4

⤇ 248 - 12 = (n - 1) × 4

⤇ 236 = (n - 1) × 4

⤇ $\rm\dfrac{236}{4}=n-1$

⤇ 59 = n - 1

⤇ 59 + 1 = n

⤇ 60 = n

⤇ n = 60

Hence,60 multiples of 4 lies between 10 and 250.

More Information :-

Sequence :- some numbers arranged in a definite order, according to a definite rule,are said to form a sequence.

• The number occuring at the nth place of sequence is called nth term which is denoted by Tn or an.