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There is ongoing research on sequence mining of transactional data. However, there are many applications where it is important to find significant intervals in which some events occur with specified strength. We study approaches to convert point-based data into intervals, thereby predicting the next occurrence of the event. We formulate four approaches for significant interval discovery and enumerate their advantages and disadvantages. We compare the performances of various approaches in terms of computation time, number of passes, coverage and interval statistics like density, interval-length and interval-confidence. We propose an approach to clustering using the significant intervals produced. Furthermore, we use these intervals, which serve as representative areas of the dataset as input to a Hybrid Apriori algorithm to mine for sequential patterns. We present the two types of interval semantics that can be used with sequential mining. We formulate an SQL-based Hybrid Apriori sequential algorithm that accepts intervals as input. Finally, we summarize the results and indicate the applications and conditions for which the various approaches can be used.