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Q.
If the mean of first n natural numbers is equal to $\frac{n + 7}{3}$, then n is equal to
Statistics
Solution:
Since, the mean of first n natural numbers is $\frac{\sum n}{n}= \frac{n\left(n+1\right)}{2n} = \frac{n+1}{2} , $ therefore, we must have
$\frac{n+1}{2} = \frac{n+7}{3}$
$ \Rightarrow 3n + 3 = 2n + 14$
$ \Rightarrow n = 11$