A Single A.M Between A And B Is - Testpoint

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A single A.M between a and b is

(a+b)/2
(a-b)/2
2ab/(a+b)
None of these

Explanation

Let, a and b two given numbers.
Let,
$A_{1}, A_{2}, A_{3} . . . . . . . . . . . . . A_{n}$ be Arithmetic means between a and b.
$a, A_{1}, A_{2}, A_{3} . . . . . . . . . . . . . A_{n}, b$ are in A.P.
$a + A_{1} + A_{2} + A_{3} + . . . . . . A_{n} + b = (\frac{n + 2}{2}) (a + b)$ (first term is =a, last term=b, number of term=n+2)

$A_{1}, A_{2}, A_{3} . . . . . . . . . . . . . A_{n} = \frac{( n + 2 ) ( a + b )}{2} - (a + b)$
$= (a + b) [\frac{n + 2}{2} - 1]$
$= (a + b) [\frac{n + 2 - 2}{2}]$
$= n (\frac{a + b}{2})$
$SH14-8-2023$

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