InterviewSolution
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InterviewSolution
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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) gt A_(2) gt A_(3) gt ...`B. `A_(1) lt A_(2) lt A_(3) lt ...`C. `A_(1) gt A_(3) gt A_(5) gt .... and A_(2) lt A_(4) lt A_(6) lt...`D. `A_(1) lt A_(3) lt A_(5)lt ....and A_(2) gt A_(4) gt A_(6) gt ...` |
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Answer» Correct Answer - A `A_(2)` is AM of `A_(1) and H_(1) and A_(1) gt H_(1)` `rArr A_(1) gt A_(2) gt H_(1)` `A_(3)` is AM of `A_(2) and H_(2) and A_(2) gt H_(2)` `{:(rArr,A_(2),gt,A_(3),gt,H_(2),),(,vdots,,vdots,,vdots,),( :.,A_(1),gt,A_(2),gt,A_(3),gt...):}` |
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