Sequential action makes up the bulk of human daily activity, and yet much remains unknown about how people learn such actions. In one motor learning paradigm, the serial reaction time (SRT) task, people are taught a consistent sequence of button presses by cueing them with the next target response. However, the SRT task only records keypress response times to a cued target, and thus it cannot reveal the full time-course of motion, including predictive movements. This paper describes a mouse movement trajectory SRT task in which the cursor must be moved to a cued location. We replicated keypress SRT results, but also found that predictive movement--before the next cue appears--increased during the experiment. Moreover, trajectory analyses revealed that people developed a centering strategy under uncertainty. In a second experiment, we made prediction explicit, no longer cueing targets. Thus, participants had to explore the response alternatives and learn via reinforcement, receiving rewards and penalties for correct and incorrect actions, respectively. Participants were not told whether the sequence of stimuli was deterministic, nor if it would repeat, nor how long it was. Given the difficulty of the task, it is unsurprising that some learners performed poorly. However, many learners performed remarkably well, and some acquired the full 10-item sequence within 10 repetitions. Comparing the high- and low-performers' detailed results in this reinforcement learning (RL) task with the first experiment's cued trajectory SRT task, we found similarities between the two tasks, suggesting that the effects in Experiment 1 are due to predictive, rather than reactive processes. Finally, we found that two standard model-free reinforcement learning models fit the high-performing participants, while the four low-performing participants provide better fit with a simple negative recency bias model.