Activities related to oil and gas production, especially deep disposal of wastewater, have led to sequences of induced earthquakes in the central U.S. This study aims to quantify damage to and seismic losses for light-frame wood buildings when subjected to sequences of induced, small to moderate magnitude, events. To conduct this investigation, one and two-story multifamily wood frame buildings are designed, and their seismic response dynamically simulated using three-dimensional (3D) nonlinear models, subjected to ground motion sequences recorded in induced events. Damage is quantified through seismic losses, which are estimated using the FEMA P-58 methodology. Results show that at levels of shaking experienced in recent earthquakes, minor damage, consisting of cracking of interior finishes and nonstructural damage to plumbing and HVAC systems is expected, which is consistent with observed damage in these events. The study also examines how expected losses and building fragility will accumulate and/or change over a sequence of earthquakes. Results indicate that damage quantified in terms of absorbed hysteretic energy tended to accumulate over the sequences; this damage corresponds to elongation or widening of cracks. However, fragility is not significantly altered by damage in a preceding event, meaning structures are not becoming more vulnerable due to existing damage. In addition, sequences of events do not change losses if the building is only repaired once at the end of the sequence, as the worsening of damage does not alter repair actions. If repairs are conducted after each event, though, total seismic losses can increase greatly from the sequence.