Question

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. $\frac{1}{2}\left(\sqrt{5}-1\right)$

Answer 1

Answer: (D)

$\frac{1}{2}\left(\sqrt{5}-1\right)$

Answer 2

Given $ar^{n-1} = ar^{n} + ar^{n+1}$ $\Rightarrow 1=r+r^{2}$ $\therefore r=\frac{\sqrt{5}-1}{2}.$