What is x in the following geometric sequence: 8,x,8,x,..

Question

Miguel writes the following: 8,x,8,x, ... He tells Alicia that he has written a geometric sequence and asks her to identify the value of x. Alicia says the value of x must be 8. Miguel says that Alicia is incorrect. Who is right?

Answer 1

 

 ratio of 1st and 2nd terms =

 ratio of 2nd and 3rd terms =

 ratio of 3rd and 4th terms =

   etc etc etc

 

 8/x = x/8

 

 x^2 = 64

 x^2 - 64 = 0

 (x+8)(x-8) = 0

  x+8 = 0  or x-8 = 0

  x= -8 or x=8

 

 

So the sequence is either 8,8,8,8,8,8.....

      OR  8,-8,8,-8,8,-8,.....

 

So Alicia partially incorrect when she says that x MUST be 8.

As you can see it can ALSO be -8