QJEEM24Mabbbc: JEE Main 2024 Mathematics - Class 11 JEEM24Mabbbc Solution: If in a G.P. of 64 terms, the sum of all the terms is 7 times…

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QJEEM24Mabbbc: JEE Main 2024 Mathematics - Class 11 JEEM24Mabbbc Solution: If in a G.P. of 64 terms, the sum of all the terms is 7 times…

If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

Multiple Choice Options

A 7
B 6
C 5
D 4

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Accepted Answer

$\begin{aligned} a + a r + a r^{2} + a r^{3} + \dots . + a r^{63} \\ = 7 (a + a r^{2} + a r^{4} \dots . + a r^{62}) \\ \Rightarrow \frac{a (1 - r^{64})}{1 - r} = \frac{7 a (1 - r^{64})}{1 - r^{2}} \\ r = 6 \end{aligned}$

QJEEM24Mabbbc: JEE Main 2024 Mathematics - Class 11 JEEM24Mabbbc Solution: If in a G.P. of 64 terms, the sum of all the terms is 7 times…

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