Question

If the mean of the first n odd natural number be n itself, then n is

• A. 1
• B. 2
• C. 3
• D. any natural number

Answer 1

Answer: (D)

any natural number

Answer 2

Mean of first n odd natural numbers = \frac{1}{n} \left\\{ 1+ 3 + 5+ ... \text{upto}\, n\, \text{terms}\right\\} = \frac{1}{n}\left\\{2\times1 + \left(n-1\right) \times2\right\\} = \frac{n^{2}}{n} = n. Hence, the given statement is true for all n $\in$ N.