In a geometric progression consisting of positive terms, each term equals the sum of the n…

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:

Accepted Answer

$a=ar+ar^2 \Rightarrow 1=r+r^2 \Rightarrow r^2+r-1=0 \Rightarrow r=\dfrac{-1\pm\sqrt5}{2}$.

Since all terms are positive, $r>0$, so $r=\dfrac{\sqrt5-1}{2}$.

Solutions · 1