Question

The sum of first 100 natural numbers is equal to
A. 5040
B. 5051
C. 5050
D. None of these

Answer 1

Hint: The first 100 natural numbers form a series of A.P. (arithmetic progression). Then find the first term, common difference and number of terms to calculate the sum of the series. So, use this concept to reach the solution of the given problem.

Complete step-by-step solution -
The first 100 natural numbers are \[1,2,3,4,...............................,98,99,100\]
Clearly, this series is in AP where the first term is 1, common difference is 1, the last term is 100 and the number of terms is 100.
We know that the sum of the terms of a series in A.P. with first term \[a\], common difference \[d\], number of terms \[n\] and last term \[l\] is given by \[S = \dfrac{n}{2}\left( {a + l} \right)\].
So, the sum of first 100 natural numbers is given by
\[
  S = \dfrac{{100}}{2}\left( {1 + 100} \right) \\
  S = 50\left( {101} \right) \\
  \therefore S = 5050 \\
\]
Hence, the sum of the first 100 natural terms is 5050.
Thus, the correct option is C.5050

Note: The sum of the series in A.P. can also be found by the formula \[S = \dfrac{n}{2}\left( {2a + \left( {n - 1} \right)d} \right)\] where, \[a\] is the first term,\[d\] is the common difference and \[n\] is the number of terms. Remember that natural numbers start from 1.