Question

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. `H_(1) gt H_(2) gt H_(3) gt ...`
B. `H_(1) lt H_(2) lt H_(3) lt ...`
C. `H_(1) gt H_(3) gt H_(5) gt ...and H_(2) lt H_(4) lt H_(6) lt ...`
D. `H_(1) lt H_(3) lt H_(5) lt...and H_(2) gt H_(4) gt H_(6) gt ....`

Answer 1

Correct Answer - B
As above `A_(1) gt H_(2) gt H_(1), A_(2) gt H_(3) gt H_(2)`
`:. H_(1) lt H_(2) lt H_(3) lt`...