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 n 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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