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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
Since, `ar^(n-1) = ar^(n) +ar^(n+1)`
`rArr 1/r = 1+r rArr r^(2) +r = 1=0`
` rArr r = (sqrt(5)-1)/2 " " [ :' r != (-5sqrt(5)-1)/2]`
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