Recent observations have demonstrated a significant growth in the integrated stellar mass of the red sequence since z=1, dominated by a steadily increasing number of galaxies with stellar masses M* < 10^11 M_sun. In this paper, we use the COMBO-17 photometric redshift survey in conjunction with deep Spitzer 24 micron data to explore the relationship between star formation and the growth of stellar mass. We calculate `star formation rate functions in four different redshift slices, splitting also into contributions from the red sequence and blue cloud for the first time. We find that the growth of stellar mass since z=1 is consistent with the integrated star formation rate. Yet, most of the stars formed are in blue cloud galaxies. If the stellar mass already in, and formed in, z<1 blue cloud galaxies were to stay in the blue cloud the total stellar mass in blue galaxies would be dramatically overproduced. We explore the expected evolution of stellar mass functions, finding that in this picture the number of massive M* > 3x10^10 M_sun blue galaxies would also be overproduced; i.e., most of the new stars formed in blue cloud galaxies are in the massive galaxies. We explore a simple truncation scenario in which these `extra blue galaxies have their star formation suppressed by an unspecified mechanism or mechanisms; simple cessation of star formation in these extra blue galaxies is approximately sufficient to build up the red sequence at M*<10^11 M_sun.
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