+0  
 
+1
34
2
avatar+312 

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
avatar+114096 
+2

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

 

cool cool cool

 Jan 5, 2021
 #2
avatar+312 
+2

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

33 Online Users

avatar
avatar
avatar