Q. In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then, the common ratio of this progression equals
A) $\frac{1}{2}\left( 1 - \sqrt{5} \right)$
B) $\frac{1}{2}\sqrt{5}$
C) $\sqrt{5}$
D) $\frac{1}{2}\left( \sqrt{5} - 1 \right)$
Explanation
(d)
Since, $ar^{n - 1} = ar^{n} + ar^{n + 1}$
$\Rightarrow \ \frac{1}{r} = 1 + r\ \ \Rightarrow r^{2} + r - 1 = 0$
$\Rightarrow \ r = \frac{\sqrt{5} - 1}{2}\ \ \ \ \ \left\lbrack \because\ \ \ r \neq \frac{- \sqrt{5} - 1}{2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.