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If a(1),a(2),a(3),"......" be in harmoni...

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

Text Solution

Verified by Experts

The correct Answer is:
D
`:.a_(1),a_(2),a_(3),"......."` are in HP.
`:.(1)/(a_(1)),(1)/(a_(2)),(1)/(a_(3)),"......."`
Let D be the common difference of this AP, then
`(1)/(a_(20))=(1)/(a_(1))+(20-1)D`
`implies D((1)/(25)-(1)/(5))/(19)=-(4)/(25xx19)`
and `(1)/(a_(n))=(1)/(a_(1))+(n-1)D=(1)/(5)-(4(n-1))/(25xx19)=((95-4n+4)/(25xx19))`
`=((99-4n)/(25xx19))lt0" " [:.a_(n)lt0]`
`implies 99-4nlt0 implies ngt24.75`.
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