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Let a(1),a(2),a(3), . . . be a harmonic ...

Let `a_(1),a_(2),a_(3), . . .` be a harmonic progression with `a_(1)=5anda_(20)=25`. The least positive integer n for which `a_(n)lt0`, is

A

22

B

23

C

24

D

25

Text Solution

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The correct Answer is:
D
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Let a_(1),a_(2),a_(3),... be in harmonic progression with a_(1)=5anda_(20)=25. The least positive integer n for which a_(n)<0 a.22 b.23 c.24 d.25

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Knowledge Check

  • If a_(1),a_(2),a_(3),"......" be in harmonic progression with a_(1)=5 and a_(20)=25 . The least positive integer n for which a_(n)lt0 is

    A
    22
    B
    23
    C
    24
    D
    25

  • Positive integers a_(1) , a_(2), a_(3) , …………... form an arithmetic progression (A. P.). If a_(1) = 5 and a_(4) = 25, then a_(6) is equal to

    A
    `2a_(1)`
    B
    `3a_(1)`
    C
    `a_(1) + a_(2)`
    D
    `a_(1) +a_(3)`

  • If a_(1), a_(2), a_(3), a_(4),…a_(n) are in harmonic progression, then a_(1) a_(2) + a_(2) a_(3) +…+ a_(n - 1).a_(n) =

    A
    `(n - 1) a_(1)a_(n)`
    B
    `na_(1) a_(n)`
    C
    `n (a_(1) + a_(n))`
    D
    none

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