A large sample of spectroscopically confirmed star-forming galaxies at redshifts 1.4 < or =, slant z sub(spec) < or =, slant 3.7, with complementary imaging in the near- and mid-IR from the ground and from the Hubble Space Telescope and Spitzer Space Telescope, is used to infer the average star formation histories (SFHs) of typical galaxies from z ~ 2 to 7. We interpret this result in the context of several systematic biases that can affect determinations of the SFR-M* relation. The average specific SFRs at z ~ 2-3 are remarkably similar within a factor of two to those measured at z gap 4, implying that the average SFH is one where SFRs increase with time. These results highlight the relative inefficiency of star formation even at early cosmic times when galaxies were first assembling.