Smart card transactions are known as a rich and continuous source of public transit data, but they miss some important attributes about trips and passengers. One of these missing attributes is the trip purpose attribute. This paper proposes a novel method to infer the trip purpose attribute from the sequences of trips of passengers instead of separate trips. The proposed method infers the trip purpose attribute (a missing attribute in the smart card data) from the temporal attributes (available attributes in the smart card data). First, the relation between the temporal attributes and the trip purpose attribute is learnt by discovering clusters of passengers in the Household Travel Survey dataset while each passenger is represented by one sequence of trips. Then, the discovered clusters are utilized to infer the trip purpose of smart card transactions by allocating each passenger to the closest clusters. The proposed method is implemented on the smart card and HTS datasets from southeast Queensland, Australia. The evaluation results showed a considerable improvement in inferring the trip purpose compared to the results published in the literature. Notably, the effect of considering the trip sequence was more significant than considering land use variables.