Sum of the First n Terms of a Sequence. The sum of the terms of a sequence is called a series. If a sequence is arithmetic or geometric there are formulas to find the sum of the first n terms, denoted Sn, without actually adding all of the terms.um of the First n Terms of a Sequence. The sum of the terms of a sequence is called a series. If a sequence is arithmetic or geometric there are formulas to find the sum of the first n terms, denoted Sn, without actually adding all of the terms.