Clinicians and researchers are increasingly interested in how best to individualize interventions. A dynamic treatment regime (DTR) is a sequence of pre-specified decision rules which guide the delivery of a course of treatments that is tailored to the changing needs of the individual. The sequential multiple-assignment randomized trial (SMART) is a research tool that can be used to inform the construction of effective DTRs. We introduce sample size formulae for SMARTs in which the primary aim is to compare two embedded DTRs using a continuous longitudinal outcome collected at three timepoints throughout the study. The method is based on a longitudinal analysis that accounts for unique features of a SMART, including modeling constraints and the over/under-representation of different sequences of treatment among participants. We also discuss extensions to a general number of timepoints. We illustrate the method using ENGAGE, a SMART aimed at developing a DTR for re-engaging patients with alcohol and/or cocaine use disorders who have dropped out of treatment.