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Properties of GP

Find x, so ...

Question

Find $x$ , so that $x, x + 2, x + 6$ are consecutive terms of a GP.

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Solution

Common ratio should be same, $\frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}}$
$\frac{x + 2}{x} = \frac{x + 6}{x + 2}$

$(x + 2)^{2} = x^{2} + 6 x$

$4 = 2 x$

$x = 2$

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