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If the second term of a geometric sequence of real numbers is -2 and the fifth term is 16, then what is the fourteenth term?

 May 4, 2020
 #1
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Let r  be  the common ratio

 

So

 

(-2)r^(5-2)  = 16

 

(-2)r^3  = 16

 

r^3  =  -16/2

 

r^3  =  - 8

 

r   = -2

 

So the 14th term is

 

(16)(-2)^(14 - 5)

 

16 (-2)^9

 

16 * (-512)  =

 

-8192

 

 

 

cool cool cool

 May 4, 2020

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