We constrain the slope of the star formation rate (SFR; log Psi) to stellar mass (log M sub(*)) relation down to log(M sub(*)/M sub(middot in circle)) = 8.4 (log(M sub(*)/M sub(middot in circle)) = 9.2) at z = 0.5 (z = 2.5) with a mass-complete sample of 39,106 star-forming galaxies selected from the 3D-HST photometric catalogs, using deep photometry in the CANDELS fields. For the first time, we find that the slope is dependent on stellar mass, such that it is steeper at low masses (log Psi is proportional to log M sub(*)) than at high masses (log Psi is proportional to (0.3-0.6) log M sub(*)). These steeper low-mass slopes are found for three different star formation indicators: the combination of the ultraviolet (UV) and infrared (IR), calibrated from a stacking analysis of Spitzer/MIPS 24 mu m imaging; beta -corrected UV SFRs; and H alpha SFRs. The normalization of the sequence evolves differently in distinct mass regimes as well: for galaxies less massive than log(M sub(*)/M sub(middot in circle)) < 10 the specific SFR (Psi/M sub(*)) is observed to be roughly self-similar with Psi/M sub(*) is proportional to (1 + z) super(1.9), whereas more massive galaxies show a stronger evolution with Psi/M sub(*) is proportional to (1 + z) super(2.2-3.5) for log(M sub(*)/M sub(middot in circle)) = 10.2-11.2. The fact that we find a steep slope of the star formation sequence for the lower mass galaxies will help reconcile theoretical galaxy formation models with the observations.