Network slicing (NS) has been identified as one of the most promising architectural technologies for future mobile network systems to meet the extremely diversified service requirements of users. In radio access networks (RAN) slicing, service provisioning for slice users becomes much more complicated than that in traditional mobile networks, as the constraints of both user physical association with base station (BS) and logical association with NS should be considered. Therefore, service provisioning in RAN slicing becomes an essential yet challenging issue for 5G and beyond systems. In this paper, we propose a unified framework for service provisioning in RAN slicing with aim of maximizing resource utilization while guaranteeing QoS of users. The framework consists of two steps. The first step is to identify a set of slice users whose QoS can be satisfied simultaneously; while the second step performs joint slice association and bandwidth allocation with aim to minimize bandwidth consumption. Numerical results show that in typical scenarios, our proposed service provisioning framework can achieve significant performance gain in terms of the number of serving users and wireless bandwidth utilization compared with traditional schemes.