MCQ
The mean of first $n$ odd natural number is :
- A$\frac{\text{n}+1}{2}$
- B$\frac{\text{n}}{2}$
- ✓$\text{n}$
- D$\text{n}^2$
✓
Answer
Correct option: C.
$\text{n}$
Mean of first $n$ odd numbers Sum of first $n$ odd number
$=\frac{\text{n}}{2}[2\text{a}+(\text{n}+1)\text{d}]$
i.e. $\{1 + 3 + 5 + 7 + ........ n\}$ term
$=\frac{\text{n}}{2}[2\times1+(\text{n}+1)\times2]$
$($Here $a = 1, d = 2)$
$=\frac{\text{n}}{2}[2+2\text{n}-2]=\frac{\text{n}}{2}\times2\text{n}=\text{n}^2$
$\therefore\text{Mean}=\frac{\text{Sum of n terms}}{\text{n}}=\frac{\text{n}^2}{\text{n}}=\text{n}$
$=\frac{\text{n}}{2}[2\text{a}+(\text{n}+1)\text{d}]$
i.e. $\{1 + 3 + 5 + 7 + ........ n\}$ term
$=\frac{\text{n}}{2}[2\times1+(\text{n}+1)\times2]$
$($Here $a = 1, d = 2)$
$=\frac{\text{n}}{2}[2+2\text{n}-2]=\frac{\text{n}}{2}\times2\text{n}=\text{n}^2$
$\therefore\text{Mean}=\frac{\text{Sum of n terms}}{\text{n}}=\frac{\text{n}^2}{\text{n}}=\text{n}$
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