jee-main 2021 Q62

jee-main · India · session4_31aug_shift1 Geometric Sequences and Series Arithmetic-Geometric Sequence Interplay
Three numbers are in an increasing geometric progression with common ratio $r$. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference $d$. If the fourth term of GP is $3 r ^ { 2 }$, then $r ^ { 2 } - d$ is equal to :
(1) $7 - \sqrt { 3 }$
(2) $7 + 3 \sqrt { 3 }$
(3) $7 - 7 \sqrt { 3 }$
(4) $7 + \sqrt { 3 }$ 
Three numbers are in an increasing geometric progression with common ratio $r$. If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference $d$. If the fourth term of GP is $3 r ^ { 2 }$, then $r ^ { 2 } - d$ is equal to :\\
(1) $7 - \sqrt { 3 }$\\
(2) $7 + 3 \sqrt { 3 }$\\
(3) $7 - 7 \sqrt { 3 }$\\
(4) $7 + \sqrt { 3 }$
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