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# Help

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95
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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.

Jan 5, 2021

#1
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The common  ratio is    (9/2)  / 3  =   9/6  = 3/2

The eighth term is

3 ( 3/2)^(8- 1)  =   3 (3/2)^7    =

3 ( 2187 / 128)  =

6561/ 128

Jan 5, 2021
#2
+303
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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 $$3\cdot(3/2)^{8-1} = 3^8/2^7 = \boxed{6561/128}$$.

Jan 5, 2021
edited by hihihi  Jan 5, 2021