By combining a tilted-pulse-intensity-front scheme using a LiNbO3 crystal and a chirped-pulse-beating method, we generated a narrowband intense terahertz (THz) pulse, which had a maximum electric field of more than 10 kV/cm at around 2 THz, a bandwidth of about 50 GHz,and frequency tunability from 0.5 to 2 THz. By performing THz-pump and near-infrared-probe experiments on GaAs quantum wells, we observed that the resonant excitation of the intraexcitonic 1s-2p transition induces a clear and large Autler-Townes splitting. Our time-resolved measurements show that the splitting energy observed in the rising edge region of electric field is larger than in the constant region. This result implies that the splitting energy depends on the time-averaged THz field over the excitonic dephasing time rather than that at the instant of the exciton creation by a probe pulse.