Determine the common ratio, the fifth, and the $n ^ { t h }$ terms of the geometric sequence. $9,9 \sqrt { 3 } , 27,27 \sqrt { 3 } , \dots$
A) $a _ { n } = 9 ( 3 ) ^ { - \cdots }$
B) $a _ { n } = 6 ( \sqrt { 3 } ) ^ { n - 1 }$
C) $a _ { n } = 9 ( \sqrt { 3 } ) ^ { n - 1 }$
D) $a _ { n } = ( \sqrt { 3 } ) ^ { n + 1 }$
E)none

Question

Quizplus · Accepted Answer

To find the common ratio, we divide each term by the preceding term. Thus, the common ratio is $\frac{9\sqrt{3}}{9} = \sqrt{3}$. The fifth term can be found by multiplying the fourth term by the common ratio. So, $27\sqrt{3} \cdot \sqrt{3} = 27 \cdot 3 = 81$. Therefore, the fifth term is 81. To find the nth term, we use the formula $a_n = a_1 r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio. Thus, $a_n = 9(\sqrt{3})^{n-1}$. Thus, the answer is $\boxed{	extbf{(C)}}$.

Determine the Common Ratio, the Fifth, and The nthn ^ { t h }nth

Determine the Common Ratio, the Fifth, and The $n ^ { t h }$