Consider the geometric sequence \( 3, \dfrac{9}{2}, \dfrac{27}{4}, \dfrac{81}{8}, \ldots\) . Find the eighth term of the sequence. Express your answer as a common fraction.
Thx CPhill also their is another way this is how I did it.
The first term is 3, and the ratio between terms is (9/2)/3=3/2 . Therefore, the eighth term of the sequence is \(3\cdot(3/2)^{8-1} = 3^8/2^7 = \boxed{6561/128}\).
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