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-

Options

A. `(1)/(2)(1-sqrt(5))`
B. `(1)/(2)sqrt(5)`
C. `sqrt(5)`
D. `(1)/(2)(sqrt(5)-1)`

Answer

D

Explanation

Let geometric progression is `a,ar,ar^(2),"…."," " [a,rgt0]`
`:.a=ar+ar^(2)`
`implies r^(2)+r+1=0 implies r=(-1pmsqrt(5))/(2)`
`:.r=(sqrt(5)-1)/(2)`.