SOLUTION: How do you find the two possible fourth values of a geometric sequence. There are two geometric sequences with 3rd term 5 and 5th term 80. What are the possible 4th terms?

Question 1091273: How do you find the two possible fourth values of a geometric sequence. There are two geometric sequences with 3rd term 5 and 5th term 80. What are the possible 4th terms?
Answer by ikleyn(52790) (Show Source): You can put this solution on YOUR website!
.

 =  = 5     for the 3-rd term.

 =  = 80    for the 5-th term.


Take the ratio

 =  = 16  =  = .


Thus you have an equation for "r":   = 16,  which has TWO solutions:  r = 4   and/or  r = -4.


So, the two possibilities for the 4-th term are

1)   =  = 5*4    = 20,   and

2)   =  = 5*(-4) = -20.

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