Which term of the GP 2, 8, 32, ldots is 13107 | vedclass

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(B) The given $GP$ is $2, 8, 32, \ldots$ where the first term $a = 2$ and the common ratio $r = \frac{8}{2} = 4$.Let $131072$ be the $n^{	ext{th}}$ t

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(B) The given $GP$ is $2, 8, 32, \ldots$ where the first term $a = 2$ and the common ratio $r = \frac{8}{2} = 4$.Let $131072$ be the $n^{	ext{th}}$ term of the $GP$.The formula for the $n^{	ext{th}}$ term is $a_n = a \cdot r^{n-1}$.Substituting the values,we get $131072 = 2 \cdot 4^{n-1}$.Dividing both sides by $2$,we get $65536 = 4^{n-1}$.Since $65536 = 4^8$,we have $4^8 = 4^{n-1}$.Equating the exponents,$n - 1 = 8$,which gives $n = 9$.Therefore,$131072$ is the $9^{	ext{th}}$ term of the $GP$.

Which term of the $GP$ $2, 8, 32, \ldots$ is $131072$ (in $^{\text{th}}$)?

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