Question

In a geometric progression whose terms are positive, any term is equal to the sum of the next two following terms. Then the common ratio is

• A. $1$
• B. About $\frac{\sqrt{5}}{2}$
• C. $\frac{\sqrt{5}-1}{2}$
• D. $\frac{1-\sqrt{5}}{2}$
• E. $\frac{2}{\sqrt{5}}$

Answer 1

Answer: (C)

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

$a{r}^n=a{r}^{n+1}+a{r}^{n+2};\therefore r^2+r=1;\therefore r=(\sqrt{5}-1)/2$.