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Question
If the mean of first n natural numbers is \[\frac{5n}{9}\], then n =
Options
5
4
9
10
Solution
Given:
Mean of first n natural number = \[\frac{5n}{9}\]
\[\Rightarrow \frac{1 + 2 + 3 + . . . + n}{n} = \frac{5n}{9}\]
\[ \Rightarrow \frac{\frac{n\left( n + 1 \right)}{2}}{n} = \frac{5n}{9}\]
\[ \Rightarrow \frac{n + 1}{2} = \frac{5n}{9}\]
\[ \Rightarrow 9n + 9 = 10n\]
\[ \Rightarrow n = 9\]
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