Which term of the following sequence: sqrt{3} | vedclass

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(C) The given sequence is $\sqrt{3}, 3, 3\sqrt{3}, \ldots$This is a geometric progression where the first term $a = \sqrt{3}$ and the common ratio $r

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(C) The given sequence is $\sqrt{3}, 3, 3\sqrt{3}, \ldots$This is a geometric progression where the first term $a = \sqrt{3}$ and the common ratio $r = \frac{3}{\sqrt{3}} = \sqrt{3}$.Let the $n^{	ext{th}}$ term of the sequence be $a_n = 729$.The formula for the $n^{	ext{th}}$ term is $a_n = a r^{n-1}$.Substituting the values,we get $\sqrt{3} \cdot (\sqrt{3})^{n-1} = 729$.This simplifies to $(\sqrt{3})^n = 729$.Since $\sqrt{3} = 3^{1/2}$,we have $(3^{1/2})^n = 3^6$.$3^{n/2} = 3^6$.Equating the exponents,$\frac{n}{2} = 6$,which gives $n = 12$.Thus,the $12^{	ext{th}}$ term of the sequence is $729$.

Which term of the following sequence: $\sqrt{3}, 3, 3\sqrt{3}, \ldots$ is $729$ (in $^{\text{th}}$)?

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