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Question
If the mean of first n natural number is 15, then n =
Options
15
30
14
29
Solution
Given:
Mean of first n natural numbers = 15
\[\Rightarrow \frac{1 + 2 + 3 + . . . + n}{n} = 15\]
\[ \Rightarrow \frac{\frac{n\left( n + 1 \right)}{2}}{n} = 15\]
\[ \Rightarrow \frac{n + 1}{2} = 15\]
\[ \Rightarrow n + 1 = 30\]
\[ \Rightarrow n = 29\]
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