Clinicians and researchers alike are increasingly interested in how best to individualize interventions. A dynamic treatment regime (DTR) is a sequence of pre-specified decision rules which guides the delivery of an individualized sequence of treatments that is tailored to specific and possibly changing needs of the individual. The sequential multiple-assignment randomized trial (SMART) is a research tool which allows for the construction of effective DTRs. We introduce a method for computing sample size for SMARTs in which the primary aim is to compare two embedded DTRs using a continuous repeated-measures outcome collected over the entire study. The sample size method is based on a longitudinal analysis that accounts for unique features of a SMART design. These features include modeling constraints and the over- or under-representation of different sequences of treatment (by design). We illustrate our methods using the ENGAGE study, a SMART aimed at developing a DTR for increasing motivation to attend treatments among alcohol- and cocaine-dependent patients.