jee-main 2015 Q67

jee-main · India · 04apr Geometric Sequences and Series Arithmetic-Geometric Sequence Interplay

If $m$ is the A.M. of two distinct real numbers $l$ and $n$ $(l, n > 1)$ and $G _ { 1 } , G _ { 2 }$ and $G _ { 3 }$ are three geometric means between $l$ and $n$, then $G _ { 1 } ^ { 4 } + 2 G _ { 2 } ^ { 4 } + G _ { 3 } ^ { 4 }$ equals
(1) $4 l ^ { 2 } m ^ { 2 } n ^ { 2 }$
(2) $4 l ^ { 2 } m n$
(3) $4 l m ^ { 2 } n$
(4) $4 l m n ^ { 2 }$

If $m$ is the A.M. of two distinct real numbers $l$ and $n$ $(l, n > 1)$ and $G _ { 1 } , G _ { 2 }$ and $G _ { 3 }$ are three geometric means between $l$ and $n$, then $G _ { 1 } ^ { 4 } + 2 G _ { 2 } ^ { 4 } + G _ { 3 } ^ { 4 }$ equals\\
(1) $4 l ^ { 2 } m ^ { 2 } n ^ { 2 }$\\
(2) $4 l ^ { 2 } m n$\\
(3) $4 l m ^ { 2 } n$\\
(4) $4 l m n ^ { 2 }$

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