Terms and Formulae
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
In a geometric sequence, the ratio r between each term and the
A series whose limit as n→∞ is a real number.
A series whose limit as n→∞ is either ∞ or - ∞.
A formula for the nth term of a sequence of the form an = some function
A sequence which is defined only for positive integers less than or equal to
a certain given integer.
A series which is defined only for positive integers less than or equal to a
certain given integer.
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
index of summation.
A sequence which is defined for all positive integers.
A series which is defined for all positive integers.
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
A function which is defined for the positive integers.
A sequence in which the terms are summed, not just listed.
- an = a1 + a2 + a3 + a4 + ... + an
. The symbol Σ
its subscript and superscript are the components of summation notation.
An element in the range of a sequence. A sequence is rarely represented by
ordered pairs, but instead by a list of its terms.
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().