What is the sum of n arithmetic means between | vedclass

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Question

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

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

Vedclass · Answer

(B) Let the $n$ arithmetic means between $a$ and $b$ be $A_1, A_2, \dots, A_n$. These $n$ terms along with $a$ and $b$ form an arithmetic progression with $n+2$ terms. The sum of these $n$ arithmetic means is given by the formula $S = \frac{n}{2}(A_1 + A_n)$. In an arithmetic progression,the sum of terms equidistant from the beginning and the end is constant,so $A_1 + A_n = a + b$. Therefore,the sum of the $n$ arithmetic means is $S = \frac{n}{2}(a + b)$.

What is the sum of $n$ arithmetic means between $a$ and $b$?

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