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Parminder Gaba
Asked: 2022-11-09T00:45:14+05:30 In:

Let `a_(n)` be the `n^(th)` term of the G.P. of positive numbers. Let `sum_(n=1)^(100) a_(2n)=alpha and sum_(n=1)^(100) a_(2n-1)=beta`, such that `a!=beta`,
then the common ratio is
A. `alpha//beta`
B. `beta//alpha`
C. `sqrt(alpha//beta)`
D. `sqrt(beta//alpha)`

Let `a_(n)` be the `n^(th)` term of the G.P. of positive numbers. Let `sum_(n=1)^(100) a_(2n)=alpha and sum_(n=1)^(100) a_(2n-1)=beta`, such that `a!=beta`,
then the common ratio is
A. `alpha//beta`
B. `beta//alpha`
C. `sqrt(alpha//beta)`
D. `sqrt(beta//alpha)`
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1 Answer

  1. Correct Answer – A
    Let a be the first term and r be the common ratio of the given G.P. Then,
    `alpha=underset(n=1)overset(100)suma_(2n)=a_(2)+a_(4)+ . . . +a_(200)=ar^(3)+ . . . .ar^(199)`
    `rArr” “alpha=ar(1+r^(2)+r^(4)+ . . .+r^(198))`
    `and,beta=underset(n=1)overset(100)suma_(2n-1)=a_(1)+a_(3)+ . . .+a_(199)=a+ar^(2)+ . . .ar^(198)`
    `rArr” “beta=a(1+r^(2)+ . . .+r^(198))`
    Clearly, `alpha//beta=r`.

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