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Let S be the sum, P be the product and R...

Let `S` be the sum, `P` be the product and `R` be the sum of the reciprocals of 3 terms of a G.P. then `P^2R^3: S^3` is equal to
(a)`1:1`

(b) `("common ratio")^n :1`
(c)`("First term")^2("common ratio")^2`
(d) None of these

Text Solution

Verified by Experts

Let the first term and common ratio of a G.P be A and R respectively.
so
we know that,
`S=(AR^(n)−1)/(R-1)`
and product,
`​P=A(AR)(AR^2)(AR^3)........(AR^(n−1))`
`⇒P=A^nR^(1+2+3+........+n−1)`
`=>A^nR^((n(n-1))/2)`
...
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Knowledge Check

  • Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a GP. Then, P^(2)R^(3) : S^(3) is equal to

    A
    `1:1`
    B
    `("common ratio")^(n):1`
    C
    `("first term")^(2) : ("common ratio")^(2)`
    D
    None of the above

  • If S be the sum, P the product and R the sum of the reciprocals of n terms of a G.P., then ((S)/(R))^(n) =

    A
    P
    B
    `P^(2)`
    C
    `P^(3)`
    D
    `sqrt(P)`

  • If S.P and R are the sum, product and sum of the reciprocals of n terms of an increasing G.P respectively and S^(n) = R^(n).P^(k) , then k is equal to

    A
    1
    B
    2
    C
    3
    D
    None of these

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