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Arithmetic Sequence and Geometric Series

Source: 1992 National High School Mathematics League, Exam One, Problem 7

February 26, 2020
arithmetic sequencegeometric series

Problem Statement

For real numbers x,y,zx,y,z, 3x,4y,5z3x,4y,5z are geometric series, 1x,1y,1z\frac{1}{x},\frac{1}{y},\frac{1}{z} are arithmetic sequence. Then xz+zx=\frac{x}{z}+\frac{z}{x}=________.
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