• Arithmetic Sequence

A sequence in which each term is a constant amount greater or less than the previous term. In this type of sequence, an+1 = an + d, where d is a constant.

• Common Ratio

In a geometric sequence, the ratio r between each term and the previous term.

• Convergent Series

A series whose limit as n→∞ is a real number.

• Divergent Series

A series whose limit as n→∞ is either or - ∞.

• Explicit Formula

A formula for the nth term of a sequence of the form an = some function of n.

• Finite Sequence

A sequence which is defined only for positive integers less than or equal to a certain given integer.

• Finite Series

A series which is defined only for positive integers less than or equal to a certain given integer.

• Geometric Sequence

A sequence in which the ratio between each term and the previous term is a constant ratio.

• Index of Summation

The variable in the subscript of Σ. For an, i is the index of summation.

• Infinite Sequence

A sequence which is defined for all positive integers.

• Infinite Series

A series which is defined for all positive integers.

• Recursive Sequence

A sequence in which a general term is defined as a function of one or more of the preceding terms. A sequence is typically defined recursively by giving the first term, and the formula for any term an+1 after the first term.

• Sequence

A function which is defined for the positive integers.

• Series

A sequence in which the terms are summed, not just listed.

• Summation Notation an = a1 + a2 + a3 + a4 + ... + an. The symbol Σ and its subscript and superscript are the components of summation notation.

• Term

An element in the range of a sequence. A sequence is rarely represented by ordered pairs, but instead by a list of its terms.

• Formulae

 Limit of an Infinite Geometric Series For a geometric sequence an = a1rn-1, where -1 < r < 1, the limit of the infinite geometric series a1rn-1 = . This is the same as the sum of the infinite geometric sequence an = a1rn-1.

 Sum of a Finite Arithmetic Sequence The sum of the first n terms of the arithmetic sequence is Sn = n( ) or Sn = na1 + (dn - d ), where d is the difference between each term.

 Sum of a Finite Geometric Sequence For a geometric sequence an = a1rn-1, the sum of the first n terms is Sn = a1( ).