During decision making between sequential stimuli, the first stimulus must be held in memory and then compared with the second. Here, we show that in systems that encode the stimuli by their firing rate, neurons can use synaptic facilitation not only to remember the first stimulus during the delay but during the presentation of the second stimulus so that they respond to a combination of the first and second stimuli, as has been found for "partial differential" neurons recorded in the ventral premotor cortex during vibrotactile flutter frequency decision making. Moreover, we show that such partial differential neurons provide important input to a subsequent attractor decision-making network that can then compare this combination of the first and second stimuli with inputs from other neurons that respond only to the second stimulus. Thus, both synaptic facilitation and neuronal attractor dynamics can account for sequential decision making in such systems in the brain.