SOLUTION: Find the tenth term of a geometric sequence if the third term is 24 and the fifth term is 32/3.

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Question 1150464: Find the tenth term of a geometric sequence if the third term is 24 and the fifth term is 32/3.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
n=3 term, 24

n=5 term, 32/3

r, the common ratio to each successive term







You can finish from this.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

            The "solution" by @josgarithmetic, giving the unique value of    to the common ratio,  is  UNCOMPLETED,
            and,  therefore,  INCORRECT.

            I came to bring the correct solution. 


 = 24

 = 


 = r^2 =  =  = , where r is the common ratio of the progression.


Therefore,  the common ratio r may have TWO possible values,  r =   and  r = .

Therefore, looking for , we should consider TWO cases.


Case 1.   r = .    Then   =  =  = .


Case 2.   r = - .    Then   =  =  = - .


ANSWER.  Under given conditions,  the 10-th term,  ,  may have one of the two values

          =    or    = - .

Solved.


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