Despite the recent interest in the neuroanatomy of inductive reasoning processes, the regional specificity within prefrontal cortex (PFC) for the different mechanisms involved in induction tasks remains to be determined. In this study, we used fMRI to investigate the contribution of PFC regions to rule acquisition (rule search and rule discovery) and rule following. Twenty-six healthy young adult participants were presented with a series of images of cards, each consisting of a set of circles numbered in sequence with one colored blue. Participants had to predict the position of the blue circle on the next card. The rules that had to be acquired pertained to the relationship among succeeding stimuli. Responses given by subjects were categorized in a series of phases either tapping rule acquisition (responses given up to and including rule discovery) or rule following (correct responses after rule acquisition). Mid-dorsolateral PFC (mid-DLPFC) was active during rule search and remained active until successful rule acquisition. By contrast, rule following was associated with activation in temporal, motor, and medial/anterior prefrontal cortex. Moreover, frontopolar cortex (FPC) was active throughout the rule acquisition and rule following phases before a rule became familiar. We attributed activation in mid-DLPFC to hypothesis generation and in FPC to integration of multiple separate inferences. The present study provides evidence that brain activation during inductive reasoning involves a complex network of frontal processes and that different subregions respond during rule acquisition and rule following phases.