the sequence given is 2, 8, 32 128, .....
the first term = 2
common ratio = the ratio between two successive term we can pick either the 3rd term from the 4th term
the general formula of recursive formula is
[tex]\begin{gathered} a_n=ar^{n-1} \\ a=\text{first term} \\ r=\text{common ratio} \\ n=\text{nth term} \end{gathered}[/tex]to find the common ratio
we can use the ratio between two successive terms
[tex]\begin{gathered} r=\frac{128}{32}=4 \\ or \\ r=\frac{32}{8}=4 \\ \text{the common difference is 4} \end{gathered}[/tex]now, we'll proceed to find the recursive formula
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=2\times4^{n-1} \\ a_n=8^{n-1} \end{gathered}[/tex]the answer is option b
