In a G.P. series consisting of positive terms, each term is equal to the sum of next two terms. Then the common ratio of this G.P. series is

\sqrt{5}

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\frac{\sqrt{5} - 1}{2}

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\frac{\sqrt{5}}{2}

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\frac{\sqrt{5} + 1}{2}

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Solution

The correct option is B $\frac{\sqrt{5} - 1}{2}$
Let first four terms of the G.P. are $a, a r, a r^{2}, a r^{3}$
Here, $r$ is the common ratio
Now, according to the question
$a = a r + a r^{2} \Rightarrow 1 = r + r^{2} (∵ a > 0) \Rightarrow r = \frac{- 1 \pm \sqrt{1 + 4}}{2} \Rightarrow r = \frac{\sqrt{5} - 1}{2} (∵ all the terms are positive)$

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In a G.P. series consisting of positive terms, each term is equal to the sum of next two terms. Then the common ratio of this G.P. series is

The correct option is B √5−12Let first four terms of the G.P. are a,ar,ar2,ar3 Here, r is the common ratio Now, according to the question a=ar+ar2⇒1=r+r2 (∵a>0)⇒r=−1±√1+42⇒r=√5−12 (∵all the terms are positive)