If $x, y, z$ are the three geometric means between $6, 54,$ then $z =$

9 \sqrt{3}

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18

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18 \sqrt{3}

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27

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Solution

The correct option is B $18 \sqrt{3}$
There are $3$ GM so the $5$ th term of the GP is $54$ while the first term is $6$
So $6 \times r^{4} = 54$
$r = \sqrt{3}$
Terms of $G P$ are $6, 6 \sqrt{3}, 18, 18 \sqrt{3}, 54$ .
$z$ will be the $3$ rd geometric mean which equals $18 \sqrt{3}$

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