Question

The number of multiples of 4 which lie between 10 and 250. From progression chapter

Answer 1

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,........248.12,16,20,24,28,32,36,40,........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)∗4248=12+(n−1)∗4

248=12+4n−4248=12+4n−4

248=4n+8248=4n+8

248–8=4n248–8=4n

240=4n240=4n

n=240/4=60n=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

12,16,20....248
a=12
d=4
an=248
a+(n-1)d=248
12+(n-1)4=248
(n-1)4=236
n-1=59
n=60