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Question
The arithmetic mean of 1, 2, 3, ... , n is
Options
\[\frac{n + 1}{2}\]
\[\frac{n - 1}{2}\]
\[\frac{n}{2}\]
\[\frac{n}{2} + 1\]
Solution
Arithmetic mean of 1, 2, 3, ... , n
\[= \frac{1 + 2 + 3 + . . . + n}{n}\]
\[ = \frac{\frac{n\left( n + 1 \right)}{2}}{n}\]
\[ = \frac{n + 1}{2}\]
Hence, the correct option is (a).
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