SOLUTION: The first term of a geometric sequence is 3. The sum of the first three terms is 129. Find the possible values of the common ratio.

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Question 849942: The first term of a geometric sequence is 3. The sum of the first three terms is 129. Find the possible values of the common ratio.
Answer by AnlytcPhil(1810) About Me  (Show Source):
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The first term of a geometric sequence is 3.
a1 = 3
The sum of the first three terms is 129.
 
   a1 + a2 + a3 = 129
a1 + a1r + a1rē = 129
   3 + 3r + 3rē = 129
 3rē + 3r - 126 = 0

Divide every term by 3

    rē + r - 42 = 0
     (r+7)(r-6) = 0
    r+7=0; r-6=0 
     r=-7;  r=6

Those are the two possible values of the common ratio. 

Checking:

So the sequence could be either 3, -21, 147, -1029, 7203, ...

The sum of the first three terms is 3-21+147 = 129

or it could be 3, 18, 108, 648, 3888, ...

The sum of the first three terms is 3+18+108 = 129
 
Edwin