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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.
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Common Ratio
In a geometric sequence, the ratio r between each term and the previous term.
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Convergent Series
A series whose limit as n→∞ is a real number.
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Divergent Series
A series whose limit as n→∞ is either ∞ or - ∞.
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Explicit Formula
A formula for the nth term of a sequence of the form an = some function of n.
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Finite Sequence
A sequence which is defined only for positive integers less than or equal to a certain given integer.
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Finite Series
A series which is defined only for positive integers less than or equal to a certain given integer.
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Geometric Sequence
A sequence in which the ratio between each term and the previous term is a constant ratio.
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Index of Summation
The variable in the subscript of Σ. For
an, i is the
index of summation.
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Infinite Sequence
A sequence which is defined for all positive integers.
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Infinite Series
A series which is defined for all positive integers.
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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.
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Sequence
A function which is defined for the positive integers.
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Series
A sequence in which the terms are summed, not just listed.
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Summation Notation
an = a1 + a2 + a3 + a4 + ... + an. The symbol Σ and
its subscript and superscript are the components of summation notation.
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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.
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.
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| 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.
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| Sum of a Finite Geometric Sequence |
For a geometric sequence an = a1rn-1, the sum of the first n
terms is Sn = a1( ).
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