Question

Which expression would give the thirteenth term Given the sequence 8, 16, 32, 64, ...,

Answer 1

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.

$\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1\\ n=13 \end{cases} \\\\\\ a_{13}=8\cdot 2^{13-1}\implies a_{13}=8\cdot 2^{12}\implies a_{13}=8\cdot 4096 \\\\\\ a_{13}=32768$