We have examined the magnetotransport properties and the structure, by Rietveld refinement of powder X-ray data, of the phases RE_1.2Sr_1.8Mn₂O₇(RE = La, Pr, Nd). We find that on cooling, La₂Sr_1.8Mn₂O₇ undergoes a transition to a nearly perfect ferromagnet with 90% magnetization at 1.45 T, as reported by earlier workers, but the Pr and Nd phases show only a small magnetization that grows gradually as the temperature is decreased. There seems to be significant correlation between electrical transport and the Jahn-Teller elongation of the apical Mn–O bonds in these systems. The elongation of the apical Mn-O bonds forces the nine-coordinate rock-salt site to be occupied preferentially by the smaller rare-earth-metal cations. This preferential occupation is reliably obtained from the X-ray refinement. All three title phases show a magnetoresistance ratio of about 4 (corresponding to a magnetoresistance, [R(0)–R(H)]/R(0), of about 75%) at a field of 7 T and temperatures around 100 K.