The sum of n arithmetic means between a and b | vedclass

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Question

(A) Let the $n$ arithmetic means between $a$ and $b$ be $A_1, A_2, \dots, A_n$.These terms form an arithmetic progression with $a$ as the first term a

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$\frac{n(a + b)}{2}$

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(A) Let the $n$ arithmetic means between $a$ and $b$ be $A_1, A_2, \dots, A_n$.These terms form an arithmetic progression with $a$ as the first term and $b$ as the $(n+2)$-th term.The sum of $n$ arithmetic means is given by $S = A_1 + A_2 + \dots + A_n$.We know that the sum of $n$ arithmetic means between $a$ and $b$ is equal to $n$ times the arithmetic mean of $a$ and $b$.Thus,$S = n 	imes \left(\frac{a + b}{2}ight) = \frac{n(a + b)}{2}$.

The sum of $n$ arithmetic means between $a$ and $b$ is:

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