Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.3 Geometric Sequences and Series - 14.3 Exercise Set - Page 912: 22

$131,072$

$2,8,32,\ldots $ The common ratio for the geometric sequence can be calculated as: $\begin{align} & r=\frac{{{a}_{2}}}{{{a}_{1}}} \\ & =\frac{8}{2} \\ & =4 \end{align}$ The 7th term of the geometric sequence can be calculated as: $\begin{align} & r={{a}_{1}}{{r}^{n-1}} \\ & =2\cdot {{4}^{9-1}} \\ & =2\cdot {{4}^{8}} \\ & =131,072 \end{align}$ Thus, the 7th term of the geometric sequence is $131,072$.