The polarized longitudinal-transverse structure function σLT′ has been measured using the p(e⃗,e′π+)n reaction in the Δ(1232) resonance region at Q2=0.40 and 0.65GeV2. No previous σLT′ data exist for this reaction channel. The kinematically complete experiment was performed at the Jefferson Lab with the CEBAF large acceptance spectrometer using longitudinally polarized electrons at an energy of 1.515GeV. A partial-wave analysis of the data shows generally better agreement with recent phenomenological models of pion electroproduction compared to the previously measured π0p channel. A fit to both π0p and π+n channels using a unitary isobar model suggests the unitarized Born terms provide a consistent description of the nonresonant background. The t-channel pion pole term is important in the π0p channel through a rescattering correction, which could be model dependent.