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Geometric Progression

Source: 1971 AHSME Problem 33

April 24, 2014
LaTeXgeometric sequencegeometric seriesAMC

Problem Statement

If PP is the product of nn quantities in Geometric Progression, SS their sum, and S′S' the sum of their reciprocals, then PP in terms of SS, S′S', and nn is
<spanclass=′latex−bold′>(A)</span>(SS′)12n<spanclass=′latex−bold′>(B)</span>(S/S′)12n<spanclass=′latex−bold′>(C)</span>(SS′)n−2<spanclass=′latex−bold′>(D)</span>(S/S′)n<spanclass=′latex−bold′>(E)</span>(S/S′)12(n−1)<span class='latex-bold'>(A) </span>(SS')^{\frac{1}{2}n}\qquad<span class='latex-bold'>(B) </span>(S/S')^{\frac{1}{2}n}\qquad<span class='latex-bold'>(C) </span>(SS')^{n-2}\qquad<span class='latex-bold'>(D) </span>(S/S')^n\qquad <span class='latex-bold'>(E) </span>(S/S')^{\frac{1}{2}(n-1)}
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