Sequencing by avidity. A reagent containing multivalent avidite substrates and an engineered polymerase are combined with DNA polonies inside a flowcell. The engineered polymerase binds to the free 3′ ends of the primer-template of a polony and selects the correct cognate avidite via base-pairing discrimination. The multivalent avidite interacts with multiple polymerases on one polony to create avidity binding that reduces the effective Kd of the avidite substrates 100-fold compared with a monovalent dye-labeled nucleotide, allowing productive binding of nanomolar concentrations. Multiple polymerase-mediated binding events per avidite ensure a long signal persistence time. Imaging of fluorescent, bound avidites enables base classification. Following detection, avidites are removed from the polonies. Extension by one base using an engineered polymerase incorporates an unlabeled, blocked nucleotide. A terminal 3′ hydroxyl is regenerated on the DNA strand, allowing repetition of the cycle.