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odolwa99
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Homework Statement
Q.: The sum of the first five terms of a geometric series is 5 and the sum of the next five terms is 1215. Find the common ratio of this series.
Homework Equations
Sn = [itex]\frac{a(r^n - 1)}{r - 1}[/itex]
The Attempt at a Solution
a + ar + ar^2 + ar^3 + ar^4 = 5
ar^5 + ar^6 + ar^7 + ar^8 + ar^9 = 1215
ar^5 + ar^6 + ar^7 + ar^8 + ar^9 = 1215
-(a + ar + ar^2 + ar^3 + ar^4) = 5
r^5 + r^5 + r^5 + r^5 + r^5 = 1210
5r^5 = 1210
r^5 = 242
r = [itex]\sqrt[5]{242}[/itex]
r [itex]\approx[/itex] 3
Answer: From textbook: 3
Please note that [itex]\sqrt[5]{243}[/itex] is exactly 3. My answer is close but still off the mark. Can someone help me figure out how to fix this? Thank you.