Question

The mean of the first $(n+1)$ natural numbers is

• A. $\frac{\left(n+2\right)}{2}$
• B. $\frac{\left(n+1\right)\left(n+2\right)}{2}$
• C. ${\left[\frac{n\left(n+1\right)}{2}\right]}^2$
• D. $\frac{\left(n+1\right)}{2}$

Answer 1

Answer: (A)

Sum of first $n$ natural numbers $=\frac{n\left(n+1\right)}{2}$
$\therefore$ Sum of first $\left(n+1\right)$ natural numbers $=\frac{\left(n+1\right)\left(n+2\right)}{2}$
$\therefore$ Mean $=\frac{\left(n+1\right)\left(n+2\right)}{2\left(n+1\right)}=\frac{n+2}{2}$