Question

What is the arithmetic mean of the first n natural numbers ?

• A. $\frac{n}{2}$
  
• B. $\frac{n+1}{2}$
  
• C. $\frac{n-1}{2}$
  
• D. n

Answer 1

The correct option is B $\frac{n+1}{2}$


We know first n natural numbers are 1, 2, 3, 4, 5, ….., n
Using above arithmetic mean formula, we can calculate the sum of first n natural numbers as $1+2+3+4+5+...+n=\frac{\left(n\right(n+1\left)\right)}{2n}=\frac{(n+1)}{2}$

Because $1+2+3+4+5+...+n=\frac{\left(n\right(n+1\left)\right)}{2}$