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Maths-

General

Easy

Question

Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of the G.P. is

$2 - \sqrt{3}$
$2 + \sqrt{3}$
$\sqrt{3} - 2$
$3 + \sqrt{2}$

The correct answer is: $2 plus square root of 3$

Let the three numbers be $a divided by r comma blank a comma blank a r$ . As the numbers form an increasing G.P., so $r greater than 1$ . It is given that $a divided by r comma blank 2 a comma blank a r$ are in A.P.
Hence,
$4 a equals fraction numerator a over denominator r end fraction plus a r$
$rightwards double arrow r to the power of 2 end exponent minus 4 r plus 1 equals 0$
$rightwards double arrow r equals 2 plus-or-minus square root of 3$
$equals 2 plus square root of 3 blank left square bracket because r greater than 1 right square bracket$

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