To find the explicit formula of a geometric sequence you use the next:
[tex]a_n=a_1\cdot r^{n-1}[/tex]
a1 is the first term in the sequence
r is the ratio between each pair of terms
2,8,32,128,...
Find r:
[tex]\begin{gathered} \frac{8}{2}=4 \\ \\ \frac{32}{8}=4 \\ \\ \frac{128}{32}=4 \end{gathered}[/tex]
Find the explicit formula:
[tex]a_n=2\cdot4^{n-1}[/tex]
To find the 10th term you substitute the n in the formula for 10:
[tex]\begin{gathered} a_{10}=2\cdot4^{10-1} \\ \\ a_{10}=2\cdot4^9_{}_{} \\ \\ a_{10}=2\cdot262144 \\ \\ a_{10}=524288 \end{gathered}[/tex]Then, the 10th term is 524,288
