Answer:
8/27
Explanation:
First, determine the common ratio of the geometric sequence:
[tex]\begin{gathered} \frac{216}{648}=\frac{1}{3} \\ \frac{72}{216}=\frac{1}{3} \\ \implies r=\frac{1}{3} \end{gathered}[/tex]The nth term of any geometric sequence is obtained using the formula:
[tex]\begin{gathered} T_n=ar^{n-1} \\ a=\text{first term} \end{gathered}[/tex]Thus, the 8th term will be:
[tex]\begin{gathered} T_8=648\times\mleft(\frac{1}{3}\mright)^{8-1} \\ _{}=648\times\frac{1^7}{3^7} \\ =\frac{648}{2187^{}} \\ T_8=\frac{8}{27} \end{gathered}[/tex]The exact value of the eighth term of the geometric sequence is 8/27.
