If $A$ be an arithmetic mean between two numbers and $S$ be the sum of $n$ arithmetic means between the same numbers, then

$S = n A$

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$A = n S$

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$A = S$

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None of these

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Solution

The correct option is A
$S = n A$

Explanation for the correct option:
Let $a$ and $b$ be the two numbers
Then, arithmetic mean, $A = \frac{(a + b)}{2}$
and, Sum of $n$ arithmetic means, $S = (\frac{n}{2}) (a + b)$
$∴ S = n A$
Hence, Option ‘A’ is Correct.

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