Find the arithmetic mean of the series: $1, 3, 5 . . . . . . . . . . . (2 n - 1)$

n

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2 n

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\frac{n}{2}

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n - 1

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Solution

The correct option is A $n$
$1, 3, 5, . . ., (2 n - 1)$
Total number of terms: $n$
Arithmetic mean: $\frac{1 + 3 + 5 + \dots + (2 n - 1)}{n}$

Using sum of first n terms of an AP:
$1 + 3 + 5 + \dots + (2 n - 1) = n^{2}$
$∴$ AM = $\frac{n^{2}}{n} = n$

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