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  4. In a G.P of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P is

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Q. In a G.P of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P is

Solution:

$a_{2}=a_{3}+a_{4}$
$ \Rightarrow a r=a r^{2}+a r^{3}$
$\Rightarrow 1=r+r^{2}$
$\therefore r=\frac{-1 \pm \sqrt{1+4}}{2}$
$=\frac{\sqrt{5}-1}{2}=2 \sin 18^{\circ}$