MCQ
The arithmetic mean of the first $n$ odd numbers is:
- ✓$\text{n}$
- B$\frac{\text{n}}{2}$
- C$\frac{\text{n - 1}}{2}$
- D$\frac{\text{n + 1}}{2}$
First $n$ odd natural numbers are $1, 3, 5, ..., (2n - 1)$
so, the required mean $ = \frac{1+3+5+ .... +({2}{\text{n-1})}}{\text{n}}$
$ = \frac{\text{n}}{2}\frac{[{1+2}{\text{n-1]}}} {\text{n}} = \frac{{\text{n}}^{2}}{\text{n}} = {\text{n}}$
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