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Question

Sum of the first ___ natural numbers is 210.


A

20

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B

21

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C

18

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D

19

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Solution

The correct option is A

20


Sum of n natural number is given by n(n+1)2.

From the given data n(n+1)2=210

n2+n420=0

Using quadratic formula, x=b±b24ac2a

Here, a=1,b=1 and c=420

n=1±(1+1680)2

n=1±412

On solving, we get n=20 and 21.

Since 'n' represents number of terms, we ignore the negative value.

Thus, n=20 i.e., sum of the first 20 natural numbers is 210.


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