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 means form an arithmetic progression with $a$ as the first term a

Vedclass · Accepted Answer

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

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(A) Let the $n$ arithmetic means between $a$ and $b$ be $A_1, A_2, \dots, A_n$.These means 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 the formula $S_n = \frac{n}{2}(A_1 + A_n)$.Since $A_1 = a + d$ and $A_n = b - d$,where $d$ is the common difference,we have $A_1 + A_n = a + b$.Therefore,the sum is $\frac{n}{2}(a + b)$.

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

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