Question

The average of first 50 natural numbers is
A. 12.25
B. 21.15
C. 25
D. 25.5

Answer 1

Hint: We will begin by writing the first 50 natural numbers, which are 1,2,3,4…..49, 50. Calculate the sum of these numbers using the sum of $n$ terms of an A.P. Then find the average of the first 50 natural numbers using the formula, ${\text{Average}} = \dfrac{{{\text{Sum of observations}}}}{{{\text{Number of observations}}}}$

Complete step-by-step answer:
Natural numbers are the numbers that help in counting.
For example, the numbers 1,2,3,4,….. are natural numbers.
Hence, the first 50 natural numbers are 1,2,3,4,…..,49,50.
We have to find the mean of the first 50 natural numbers.
The mean is calculated by dividing the sum of observations by the number of observations.
The numbers 1,2,3,….48,49,50 are in A.P. where the first term is 1 and the common difference is 1.
We know that the sum of $n$ terms of an A.P. is given by \[{S_n} = \dfrac{n}{2}\left( {a + {a_n}} \right)\], where $a$ is the first term and ${a_n}$ is the last term.
Then, the sum of first fifty natural numbers is
 $
   \Rightarrow \dfrac{{50}}{2}\left( {1 + 50} \right) \\
   \Rightarrow 25\left( {51} \right) \\
   \Rightarrow 1275 \\
$
We will divide this by the number of observations, that is by 50 to find the required average.
$\dfrac{{1275}}{{50}} = 25.5$
Hence, the average of first 50 natural numbers is 25.5
Thus, option D is correct.

Note: Average is also known as the mean of the data. Many students consider 0 as a natural number, which is incorrect. The smallest natural number is 1, while 0 is the smallest whole number. We can also calculate the sum of $n$ terms of an A.P. using the formula, $\dfrac{n}{2}\left( {2a + \left( {n - 1} \right)d} \right)$, where $a$ is the first term and $d$ is the common difference.