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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 `n >2,`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
a. `A_(1)gtA_(2)gtA_(3)gt"......."`
b. `A_(1)ltA_(2)ltA_(3)lt"......."`
c. `A_(1)gtA_(3)gtA_(5)gt"......."" and " A_(2)ltA_(4)ltA_(6)lt"......."`
d. `A_(1)ltA_(3)ltA_(5)lt"......."" and " A_(2)gtA_(4)gtA_(6)gt"......."`

A

`A_(1)gtA_(2)gtA_(3)gt"......."`

B

`A_(1)ltA_(2)ltA_(3)lt"......."`

C

`A_(1)gtA_(3)gtA_(5)gt"......."" and " A_(2)ltA_(4)ltA_(6)lt"......."`

D

`A_(1)ltA_(3)ltA_(5)lt"......."" and " A_(2)gtA_(4)gtA_(6)gt"......."`

Text Solution

Verified by Experts

The correct Answer is:
A
`A_(2)" is " AM" of "A_(1)" and "H_(1)" and "A_(1)gtH_(1)`
`implies A_(1)gtA_(2)gtH_(1)`
`A_(3)" is " AM" of "A_(2)" and "H_(2)" and "A_(2)gtH_(2)`
`implies A_(2)gtA_(3)gtH_(2)`
`:. A_(1)gtA_(2)gtA_(3)gt"…….."`
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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"......."

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