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Let`A_(1),G_(1),H_(1)` denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For `nge2`, let `A_(n-1),G_(n-1)" and "H_(n-1)` has arithmetic,geometric and harmonic means as `A_(n),G_(n),H_(n)` respectively.
Which of the following statement is correct?

A

`H_(1)gtH_(2)gtH_(3)gt"......."`

B

`H_(1)ltH_(2)ltH_(3)lt"......."`

C

`H_(1)gtH_(3)gtH_(5)gt"......." " and " H_(2)ltH_(4)ltH_(6)lt"......."`

D

`H_(1)ltH_(3)ltH_(5)lt"......."" and " H_(2)gtH_(4)gtH_(6)gt"......."`

Text Solution

Verified by Experts

The correct Answer is:
B
As above`A_(1)gtH_(2)gtH_(1),A_(1)gtH_(3)gtH_(2)`
`:.H_(1)ltH_(2)ltH_(3)lt"......"`
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  2. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  3. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

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  4. In a G.P of positive terms if any term is equal to the sum of the next...

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  6. The first two terms of a geometric progression add up to 12. The sum o...

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  7. If the sum of first n terms of an A.P. is cn^(2) then the sum of squar...

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  8. The sum to infinity of the series 1+2/3+6/3^2+14/3^4+...is

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  9. Let Sk,k=1, 2, …. 100 denote the sum of the infinite geometric series ...

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  11. A person is to count 4500 currency notes. Let an denote the number of ...

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  13. A man saves ₹ 200 in each of the first three months of his servies.In ...

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  14. Let a(n) be the nth term of an AP, if sum(r=1)^(100)a(2r)= alpha " and...

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  15. Let,a1,a2a,a3,…. be in harmonic progression with a1=5 " and " a(20)=25...

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  16. Statement 1: The sum of the series 1""+""(1""+""2""+""4)""+""(4""+""...

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  17. If 100 times the 100 th term of an A.P with non- zero common differenc...

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  18. If x,y,z are in AP and tan^(-1)x,tan^(-1)y,tan^(-1)z are also in AP, ...

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  19. The sum of first 20 terms of the sequence 0.7 ,0.77 , 0.777 …., is

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