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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

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

D

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

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • 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 is equal to

    A
    `1/2(1-sqrt5)`
    B
    `1/2sqrt5`
    C
    `sqrt5`
    D
    `1/2(sqrt5-1)`

  • In a GP of positive terms, if any term is equal to the sum of the next terms. Then the common ratio of the GP is

    A
    `sin 18^(@)`
    B
    `2 cos 18^(@)`
    C
    `cos 18^(@)`
    D
    `2 sin 18^(@)`

  • In a GP of positive terms, any term is equal to one-third of the sum of next two terms. What is the common ratio of the GP?

    A
    `(sqrt(13)+1)/(2)`
    B
    `(sqrt(13)-1)/(2)`
    C
    `(sqrt(13)+1)/(3)`
    D
    `sqrt(13)`

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