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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Sequences and Series

NDA 2012 · Mathematics · Sequences and Series

What is the mean of first n odd natural numbers?

What is the mean of first nn odd natural numbers?

Options

  1. Ann
  2. B(n+1)/2(n+1) / 2
  3. Cn(n+1)/2n(n+1) / 2
  4. Dn+1n+1

Correct answer

A. nn

Step-by-step solution

Sum of first nn odd natural numbers S=1+3+5+………+(2n−1)S=n2(1+2n−1)=n2\begin{aligned} & \mathrm{S}=1+3+5+\ldots \ldots \ldots+(2 n-1) \\ & \mathrm{S}=\frac{n}{2}(1+2 n-1)=n^2\end{aligned} mean = sum of observations  number of observations =n2n=n=\frac{\text{ sum of observations }}{\text{ number of observations }}=\frac{n^2}{n}=n
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