Finite Sequence

A function whose domain is the set of the first n positive integers.

Infinite Sequence

Finite series, or partial sum

S_n

the sum of the first n terms of  sequence

Infinite series

the sum of all of the terms in an infinite sequence

Recursive Definition for a Sequence

a₁ = the value of the first term

a_k = some function of a_k-1

or

a₁=the value of the first term

a_k+1 = some function of a_k

Geometric Sequence

A sequence in which the ratio of successive terms is the same. This constant ratio is r.

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Formula for Finite Sum of a

Geometric Sequence, S_n

Formula for the nth term of a Geometric Sequence

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Formula for an Infinite Geometric series, S

when |r|<1

Formula for the nth term of an Arithmetic Sequence

Arithmetic Sequence

A sequence in which the difference between consecutive terms is the same.

The common difference is d

Formula for the sum of the first n terms of an Arithmetic Sequence (S_n)