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Q.

What is the sum of the first 100 natural numbers?


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a

-5050

b

5005

c

5050

d

-5005  

answer is C.

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Detailed Solution

It is given the natural numbers 1,2,3……100.
The natural number form an AP with first term 1 and common difference 1.
So, we have,
a=1,d=1.
We know that sum of first n terms of an AP is given as,
Sn=n22a+n-1d.
Putting the value of a = 1 and d = 1, we get
Sn =n2[2×1+(n-1)×1]  Sn=n2[2+n-1] Sn=n2[n+1]
 Sn=n(n+1)2   [1]
Substituting n=100 in [1], we get
 S100=100(100+1)2
S100=50×101
S100=5050 Therefore, the sum of the first 100 natural numbers is 5050.
Hence, the correct option is 3.
 
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What is the sum of the first 100 natural numbers?