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Geometric Series

Source: 1998 National High School Mathematics League, Exam One, Problem 3

March 9, 2020
geometric series

Problem Statement

For geometric series (an)(a_n) with all items real, if S10=10,S30=70S_{10}=10,S_{30}=70, then S40=S_{40}= (A)150(B)−200(C)150 or −200(D)−50 or 400\text{(A)}150\qquad\text{(B)}-200\qquad\text{(C)}150\text{ or }-200\qquad\text{(D)}-50\text{ or }400 Note: Sn=∑i=1naiS_n=\sum_{i=1}^{n}a_i.
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