{\displaystyle B_{1}=-{\frac {1}{2}}.} An arithmetic progression is one of the common examples of sequence and series. B n {\displaystyle B_{n}} is a Bernoulli number, and here, B 1 = − 1 2. If you wish to find any term (also known as the {n^{th}} term) in the arithmetic sequence, the arithmetic sequence formula should help you to do so. Arithmetic and Geometric Series Definitions: First term: a 1 Nth term: a n Number of terms in the series: n Sum of the first n terms: S n Difference between successive terms: d Common ratio: q Sum to infinity: S Arithmetic Series Formulas: a a n dn = … In an Arithmetic Sequence the difference between one term and the next is a constant.. An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series is the sum of all elements. E n {\displaystyle E_{n}} is an Euler number. Series Formulas 1. This list of mathematical series contains formulae for finite and infinite sums. In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The Formula of Arithmetic Sequence. The study of series is a major part of calculus and its generalization, mathematical analysis.Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. A Sequence is a set of things (usually numbers) that are in order.. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for more details.. Arithmetic Sequence. The critical step is to be able to identify or extract known values from the problem that will eventually be substituted into the formula … Sequence and series is one of the basic topics in Arithmetic. It can be used in conjunction with other tools for evaluating sums. Here, 0 0 {\displaystyle 0^{0}} is taken to have the value 1 {\displaystyle 1} B n ( x ) {\displaystyle B_{n}(x)} is a Bernoulli polynomial. Arithmetic Sequences and Sums Sequence.