The only way to know for sure is to ask your professor. This information may also be found in your syllabus for a class, or material about the assignment you're working on.
Most of the time, classes in certain disciplines consistently use the same citation style. This list at the OWL @ Purdue gives a run down of which disciplines use which style.
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All scholarly work (and yes, this includes your term papers), owes something to previous work. Citing our sources when we write is an agreed-upon way to acknowledge the people who have helped us shape our ideas, or argue our points. It is required because failing to cite our sources properly (intentionally or accidentally) is passing off others' ideas as our own. This is stealing or plagiarism.
The good news is that citing your sources doesn't have to be difficult. Pick the citation style that applies to your discipline from the tabs above to get started. Remember that your friendly librarians are always here to help you if you get stuck!