With the increasing adoption of big data, sequential pattern mining (SPM) –a technique for identifying frequent patterns within sequential data– has attracted significant attention. As the optimal support threshold depends on the dataset, interactive SPM, which allows users to dynamically adjust algorithm parameters, is essential for practical analysis. However, conventional interactive SPM methods rely on known frequent patterns and often overlook closed frequent patterns. This limitation may hinder analytical efficiency, especially when comprehensive yet concise pattern sets are required. In domains, such as medical records, closed frequent patterns alone can offer a comprehensive understanding of treatment processes. In this study, we propose a method to accelerate interactive SPM by focusing on closed frequent patterns. Our approach enhances pattern analysis by efficiently reusing previously mined closed patterns. Furthermore, we demonstrate the effectiveness of incorporating closed pattern consideration through evaluations on public datasets. The results demonstrate improved efficiency in pattern discovery compared to conventional approaches.