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.

Options

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"......."`

Answer

A

Explanation

`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"…….."`