if you notice, 8, 16, 32, 64 <--- 8 * 2 is 16, 16 * 2 is 32 and so on.
so, you get the next term's value by simply multiplying the "current term" by 2. So is a geometric sequence then.
therefore, the "common ratio" or multiplier is 2, and the first term's value is 8.
[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\
a_n=a_1\cdot r^{n-1}\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=2\\
a_1\\
n=13
\end{cases}
\\\\\\
a_{13}=8\cdot 2^{13-1}\implies a_{13}=8\cdot 2^{12}\implies a_{13}=8\cdot 4096
\\\\\\
a_{13}=32768[/tex]
