Clinicians and researchers alike are increasingly interested in how best to individualize interventions. A dynamic treatment regimen (DTR) is a sequence of pre-specified decision rules which guide the delivery of a sequence of treatments that are tailored to the changing needs of the individual. Sequentially-randomized trials are a research tool that can be used to inform the construction of effective DTRs. We introduce a method for computing sample size for such trials 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 the trial 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 sequentially-randomized trial aimed at developing a DTR for re-engaging patients with alcohol and cocaine use disorders who have dropped out of treatment.