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The fifth term of a geometric sequence of positive numbers is $11$ and the eleventh term is $5$. What is the eighth term of the sequence? Express your answer in simplest radical form.

 Jun 19, 2019
 #1
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Let a1 be the first term

 

So....we have that

 

11 / 5  =   a1 (r)^4 / [ a1 (r)^10]

 

11/5  =  r^4/r^10

 

11/5 =  1/ r^6

 

r^6  = (5/11)

 

r = (5/11)^(1/6)

 

 

So...the eighth term is

 

11 * [(5/11)^(1/6)]^3   =

 

11 ( 5/11)^(1/2) =

 

11 √5/ √11  =

 

√11*√5  =

 

√55

 

 

 

cool cool cool

 Jun 19, 2019

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