term of a sequence

A term is a single number sitting at one position in a sequence. If the sequence is a row of mailboxes, each term is the number tucked inside one box, and the box's house number is the term's position.

Terms are labelled by their position with a subscript: a_1 (or sometimes a_0) is the first term, a_2 the second, and a_n the general term at position n. The phrase “the n-th term” usually means a formula for a_n that works for every n at once.

Be careful with two nearby ideas: the term a_n is a number, while n is the position (an index). Asking “which term equals 50?” means solving a_n = 50 for n; asking “what is the 50th term?” means computing a_50.