A sequence is a set of ordered numbers. For example, the sequence 2, 4, 6, 8, ... has 2 as its first term, 4 as its second, etc. The nth term in a sequence is usually called sn. The terms of a sequence may be arbitrary, or they may be defined by a formula, such as sn = 2n.
In general, n starts at 1 for sequences, but there are times when it is convenient for n to start at 0, in which case the first term is s0. If we add up the first n terms of a sequence we get a partial sum, usually referred to as Sn (i.e., with a capital letter).