The mean of first n odd natural number is

Question:

The mean of first n odd natural number is

(a) $\frac{n+1}{2}$

(b) $\frac{n}{2}$

(c) $n$

 

(d) $n^{2}$

Solution:

The first odd natural numbers are 1, 3, 5, ... , (2n − 1).

$\therefore$ Mean of first $n$ odd natural numbers

$=\frac{1+3+5+\ldots+(2 n-1)}{n}$

$=\frac{\frac{n}{2}(1+2 n-1)}{n} \quad\left[S_{n}=\frac{n}{2}(a+l)\right]$

$=\frac{2 n}{2}$

 

$=n$

Hence, the correct answer is (c).

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