A sequence is a list of numbers, called terms, written in a specific order.<\/li>\n\t
Explicit formulas define each term of a sequence using the position of the term.<\/li>\n\t
An explicit formula for the [latex]n\\text{th}[\/latex] term of a sequence can be written by analyzing the pattern of several terms.<\/li>\n\t
Recursive formulas define each term of a sequence using previous terms.<\/li>\n\t
Recursive formulas must state the initial term, or terms, of a sequence.<\/li>\n\t
A set of terms can be written by using a recursive formula.<\/li>\n\t
A factorial is a mathematical operation that can be defined recursively.<\/li>\n\t
The factorial of [latex]n[\/latex] is the product of all integers from 1 to [latex]n[\/latex]<\/li>\n<\/ul>
Glossary<\/h2>\n
explicit formula<\/dt>
a formula that defines each term of a sequence in terms of its position in the sequence<\/dd><\/dl>
finite sequence<\/dt>
a function whose domain consists of a finite subset of the positive integers [latex]\\left\\{1,2,\\dots n\\right\\}[\/latex] for some positive integer [latex]n[\/latex]<\/dd><\/dl>
infinite sequence<\/dt>
a function whose domain is the set of positive integers<\/dd><\/dl>
n factorial<\/dt>
the product of all the positive integers from 1 to [latex]n[\/latex]<\/dd><\/dl>
nth term of a sequence<\/dt>
a formula for the general term of a sequence<\/dd><\/dl>
recursive formula<\/dt>
a formula that defines each term of a sequence using previous term(s)<\/dd><\/dl>
sequence<\/dt>
a function whose domain is a subset of the positive integers<\/dd><\/dl>
term<\/dt>
a number in a sequence<\/dd><\/dl>\u00a0","rendered":"
A sequence is a list of numbers, called terms, written in a specific order.<\/li>\n
Explicit formulas define each term of a sequence using the position of the term.<\/li>\n
An explicit formula for the [latex]n\\text{th}[\/latex] term of a sequence can be written by analyzing the pattern of several terms.<\/li>\n
Recursive formulas define each term of a sequence using previous terms.<\/li>\n
Recursive formulas must state the initial term, or terms, of a sequence.<\/li>\n
A set of terms can be written by using a recursive formula.<\/li>\n
A factorial is a mathematical operation that can be defined recursively.<\/li>\n
The factorial of [latex]n[\/latex] is the product of all integers from 1 to [latex]n[\/latex]<\/li>\n<\/ul>\n
Glossary<\/h2>\n
\n
explicit formula<\/dt>\n
a formula that defines each term of a sequence in terms of its position in the sequence<\/dd>\n<\/dl>\n
\n
finite sequence<\/dt>\n
a function whose domain consists of a finite subset of the positive integers [latex]\\left\\{1,2,\\dots n\\right\\}[\/latex] for some positive integer [latex]n[\/latex]<\/dd>\n<\/dl>\n
\n
infinite sequence<\/dt>\n
a function whose domain is the set of positive integers<\/dd>\n<\/dl>\n
\n
n factorial<\/dt>\n
the product of all the positive integers from 1 to [latex]n[\/latex]<\/dd>\n<\/dl>\n
\n
nth term of a sequence<\/dt>\n
a formula for the general term of a sequence<\/dd>\n<\/dl>\n
\n
recursive formula<\/dt>\n
a formula that defines each term of a sequence using previous term(s)<\/dd>\n<\/dl>\n
\n
sequence<\/dt>\n
a function whose domain is a subset of the positive integers<\/dd>\n<\/dl>\n