Question

In a G.P. of positive terms, any terms is equal to the sum of next two terms, then common ratio of the G.P. is

• A. $cos{18}^{\circ }$
• B. $sin{18}^{\circ }$
• C. $2cos{18}^{\circ }$
• D. $2sin{18}^{\circ }$

Answer 1

The correct option is D $2sin{18}^{\circ }$

Let any three terms be $\frac{a}{r},a,ar$
Then, $\frac{a}{r}=a+ar$
$\Rightarrow r(r+1)=1$
$\Rightarrow r^2+r-1=0$
$\Rightarrow r=\frac{-1\pm \sqrt{5}}{2}$
Given: $r>0$

$\therefore r=\frac{-1+\sqrt{5}}{2}$

$=2sin{18}^{\circ }$