  We present an asteroseismic analysis of 33 solar-type stars observed in short
cadence during Campaigns (C) 1-3 of the NASA K2 mission. We were able to
extract both average seismic parameters and individual mode frequencies for
stars with dominant frequencies up to ~3300{\mu}Hz, and we find that data for
some targets are good enough to allow for a measurement of the rotational
splitting. Modelling of the extracted parameters is performed by using
grid-based methods using average parameters and individual frequencies together
with spectroscopic parameters. For the target selection in C3, stars were
chosen as in C1 and C2 to cover a wide range in parameter space to better
understand the performance and noise characteristics. For C3 we still detected
oscillations in 73% of the observed stars that we proposed. Future K2 campaigns
hold great promise for the study of nearby clusters and the chemical evolution
and age-metallicity relation of nearby field stars in the solar neighbourhood.
We expect oscillations to be detected in ~388 short-cadence targets if the K2
mission continues until C18, which will greatly complement the ~500 detections
of solar-like oscillations made for short-cadence targets during the nominal
Kepler mission. For ~30-40 of these, including several members of the Hyades
open cluster, we furthermore expect that inference from interferometry should
be possible.
