SOLUTION: In a geometric series, t1=3 and s3=21. Find the common ratio and the sum of the first 7 terms.

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Question 758581: In a geometric series, t1=3 and s3=21. Find the common ratio and the sum of the first 7 terms.
Answer by reviewermath(1029) About Me  (Show Source):
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Q:
In a geometric series, t%5B1%5D = 3 and S%5B3%5D = 21. Find the common ratio and the sum of the first 7 terms.
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A:
3 + 3r + 3r%5E2 = 21
1 + r + r%5E2 = 7
r%5E2 + r - 6 = 0
(r + 3)(r - 2) = 0
r = 2 OR -3
The common ratio, r is highlight%282%29 or highlight%28-3%29.
If the common ratio is 2, then the sum of the first 7 terms is:
3 + 6 + 12 + 24 + 48 + 96 + 192 = highlight%28381%29.
If the common ratio is -3, then the sum of the first 7 terms is:
3 + (-9) + 27 + (-81) + 243 + (-729) + 2187 = highlight%281641%29