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in a geometric progression consisting o...

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

`(1)/(2)(1-sqrt(5))`

B

`(1)/(2)sqrt(5)`

C

`sqrt(5)`

D

`(1)/(2)(sqrt(5)-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
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)`.
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