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We present an asteroseismic analysis of 33 solar-type stars observed in shortcadence during Campaigns (C) 1-3 of the NASA K2 mission. We were able toextract both average seismic parameters and individual mode frequencies forstars with dominant frequencies up to ~3300{\mu}Hz, and we find that data forsome targets are good enough to allow for a measurement of the rotationalsplitting. Modelling of the extracted parameters is performed by usinggrid-based methods using average parameters and individual frequencies togetherwith spectroscopic parameters. For the target selection in C3, stars werechosen as in C1 and C2 to cover a wide range in parameter space to betterunderstand the performance and noise characteristics. For C3 we still detectedoscillations in 73% of the observed stars that we proposed. Future K2 campaignshold great promise for the study of nearby clusters and the chemical evolutionand age-metallicity relation of nearby field stars in the solar neighbourhood.We expect oscillations to be detected in ~388 short-cadence targets if the K2mission continues until C18, which will greatly complement the ~500 detectionsof solar-like oscillations made for short-cadence targets during the nominalKepler mission. For ~30-40 of these, including several members of the Hyadesopen cluster, we furthermore expect that inference from interferometry shouldbe possible.

Asteroseismic properties of solar-type stars observed with the NASA K2 mission: results from Campaigns 1-3 and prospects for future observations