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Find the common ratio of the geometric sequence $16,24,36,54, \ldots$ Then express each sequence in the form $a_{n}=a_{1} r^{n-1}$ and find the eighth term of the sequence.
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\begin{aligned} &\text { Since } r=\frac{a_{2}}{a_{1}}=\frac{24}{16}=\frac{3}{2} \\ &\text { Then } a_{n}=16\left(\frac{3}{2}\right)^{n-1} \end{aligned}
Therefore, the eighth term of the sequence is
\begin{aligned} a_{8} &=16\left(\frac{3}{2}\right)^{8-1} \\ &=16\left(\frac{3}{2}\right)^{7} \\ &=\frac{2187}{8} \end{aligned}
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