The DarkSide-50 dark matter search reports the first results obtained using a target of low-radioactivity argon extracted from underground sources. The experiment is located at the Laboratori Nazionali del Gran Sasso and uses a two-phase time projection chamber as a detector. A total of 155 kg of low radioactivity argon has been obtained, and we have determined that underground argon is depleted in Ar-39 by a factor (1.4 +- 0.2) x 10^3 relative to atmospheric argon. The underground argon is also found to contain (2.05 +- 0.13) mBq/kg of Kr-85. We find no evidence for dark matter in the form of WIMPs in 70.9 live-days of data with a fiducial mass of (36.9 +- 0.6) kg. When combined with our preceding search with an atmospheric argon target, we set a 90 % C.L. upper limit on the WIMP-nucleon spin-independent cross section of 2.0 x 10^-44 cm^2 (8.6 x 10^-44 cm^2, 8.0 x 10^-43 cm^2) for a WIMP mass of 100 GeV/c^2 (1 TeV/c^2 , 10 TeV/c^2).
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