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In a geometric progression consisting...

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 (1) `1/2(1-sqrt(5))` (2) `1/2sqrt(5)` (3) `sqrt(5)` (4) `1/2(sqrt(5)-1)`

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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 geometrical progression first term and common ratio are both (1)/(3) (1 sqrt"" 3 + i) . Then the absolute value of the nth term of the progression is

    A
    `2^(n)`
    B
    `4^(n)`
    C
    1
    D
    none of these

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    If three successive terms of G.P from the sides of a triangle then show that common ratio ' r' satisfies the inequality 1/2 (sqrt(5)-1) lt r lt 1/2 (sqrt(5)+1) .

    If common ratio of a geometric progression is positive then maximum value of the ratio of second term to the sum of first 3 terms equals

    1/(sqrt(2)+sqrt(3)+sqrt(5))+1/(sqrt(2)+sqrt(3)-sqrt(5))

    (1)/(sqrt(2)+sqrt(3)-sqrt(5))+(1)/(sqrt(2)-sqrt(3)-sqrt(5))

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