jee-main 2023 Q64

jee-main · India · session2_13apr_shift2 Geometric Sequences and Series Finite Geometric Sum and Term Relationships
Let $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$ be a G.P. of increasing positive numbers. Let the sum of its $6 ^ { \text {th} }$ and $8 ^ { \text {th} }$ terms be 2 and the product of its $3 ^ { \text {rd} }$ and $5 ^ { \text {th} }$ terms be $\frac { 1 } { 9 }$. Then $6 ( a _ { 2 } + a _ { 4 } )( a _ { 4 } + a _ { 6 } )$ is equal to
(1) 3
(2) $3 \sqrt { 3 }$
(3) 2
(4) $2 \sqrt { 2 }$
Let $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$ be a G.P. of increasing positive numbers. Let the sum of its $6 ^ { \text {th} }$ and $8 ^ { \text {th} }$ terms be 2 and the product of its $3 ^ { \text {rd} }$ and $5 ^ { \text {th} }$ terms be $\frac { 1 } { 9 }$. Then $6 ( a _ { 2 } + a _ { 4 } )( a _ { 4 } + a _ { 6 } )$ is equal to\\
(1) 3\\
(2) $3 \sqrt { 3 }$\\
(3) 2\\
(4) $2 \sqrt { 2 }$