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Geometric Progression

If x,y and z ...

Question

If $x, y$ and $z$ are three consecutive terms of a G.P such that $x y z = 8,$ then $y$ equals ____.

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Solution

Given that the three consecutive terms of the GP are $x, y$ and $z .$
Let $x = \frac{a}{r}, y = a$ and $z = a r .$
$x y z = 8 \Rightarrow \frac{a}{r} \times a \times a r = 8.$
$\Rightarrow a^{3} = 8$
$\Rightarrow a = 2$
$∴ y = a = 2.$

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