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Maths-

General

Easy

Question

If $A subscript 1 end subscript comma blank A subscript 2 end subscript$ are two A $blank times$ M’s between $a$ and $b$ and $G subscript 1 end subscript comma blank G subscript 2 end subscript$ are two GM’s between $a$ and $b$ then $fraction numerator A subscript 1 end subscript plus A subscript 2 end subscript over denominator G subscript 1 end subscript G subscript 2 end subscript end fraction$ is

$\frac{a + b}{a b}$
$\frac{a + b}{2}$
$\frac{a + b}{a - b}$
None of these

The correct answer is: $fraction numerator a plus b over denominator a b end fraction$

$a comma blank A subscript 1 end subscript comma blank A subscript 2 end subscript comma blank b$ are in AP
$therefore blank A subscript 1 end subscript minus a equals b minus A subscript 2 end subscript$
$rightwards double arrow blank A subscript 1 end subscript plus A subscript 2 end subscript equals a plus b$
And $a comma blank G subscript 1 end subscript comma blank G subscript 2 end subscript comma b$ are in GP.
$therefore blank fraction numerator G subscript 1 end subscript over denominator a end fraction equals fraction numerator b over denominator G subscript 2 end subscript end fraction$
$rightwards double arrow G subscript 1 end subscript G subscript 2 end subscript equals a b$
$therefore blank fraction numerator A subscript 1 end subscript plus A subscript 2 end subscript over denominator G subscript 1 end subscript G subscript 2 end subscript end fraction equals fraction numerator a plus b over denominator a b end fraction$

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