SOLUTION: The third term of a geometric sequence is 3 and the 6th term is 1/9? Find the first term.

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Question 1086032: The third term of a geometric sequence is 3 and the 6th term is 1/9? Find the first term.
Found 3 solutions by Fombitz, ikleyn, MathTherapy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!


Subtracting,




So then,
Answer by ikleyn(52775)   (Show Source): You can put this solution on YOUR website!
.
 =  = 3,     (1)

 =  = .     (2)


Divide eq(2) by eq(1) (both sides). You will get 

 =  =  =  = ,

which implies  

r = .


Thus we found the common ratio. It is r = .


Then from  (1)   =  =  = 27.


The progression is 27, 9, 3, 1, , .

Answer. = 27.

Solved.



Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

The third term of a geometric sequence is 3 and the 6th term is 1/9? Find the first term.
First term, or 

IGNORE anyone who says otherwise!! 

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