The question is given from ncert Book of class 10th Chapter no. 5 Ex. 5.2 Q. 14. In the following question you have to find that how many multiples of 4 lie b/w 10 and 250. Give the answer of the above question in brief.
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Solution:
The 1st multiple of 4 that is greater than 10 is 12.
Next multiple will be 16.
i.e, the series formed as:
12, 16, 20, 24, …
All of them are divisible by 4 and all these are terms of an A.P. with 1st term as 12 and c.d as 4.
The remainder will be 2, when we divide 250 by 4.
i.e, 250 − 2 = 248 is divisible by 4.
Now, 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
As we all know,
an = a+(n−1)d
248 = 12+(n-1)×4
236/4 = n-1
59 = n-1
n = 60
i.e there are 60 multiples of 4 b/w 10 & 250.