{"id":2434,"date":"2016-11-03T22:16:10","date_gmt":"2016-11-03T22:16:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&p=2434"},"modified":"2017-04-04T20:00:01","modified_gmt":"2017-04-04T20:00:01","slug":"summary-sequences-and-their-notations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/summary-sequences-and-their-notations\/","title":{"raw":"Summary: Sequences and Their Notations","rendered":"Summary: Sequences and Their Notations"},"content":{"raw":"
A sequence is a list of numbers, called terms, written in a specific order.<\/li>\r\n \t
Explicit formulas define each term of a sequence using the position of the term.<\/li>\r\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>\r\n \t
Recursive formulas define each term of a sequence using previous terms.<\/li>\r\n \t
Recursive formulas must state the initial term, or terms, of a sequence.<\/li>\r\n \t
A set of terms can be written by using a recursive formula.<\/li>\r\n \t
A factorial is a mathematical operation that can be defined recursively.<\/li>\r\n \t
The factorial of [latex]n[\/latex] is the product of all integers from 1 to [latex]n[\/latex]<\/li>\r\n<\/ul>\r\n
Glossary<\/h2>\r\nexplicit formula<\/strong> a formula that defines each term of a sequence in terms of its position in the sequence\r\n\r\nfinite sequence<\/strong> 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]\r\n\r\ninfinite sequence<\/strong> a function whose domain is the set of positive integers\r\n\r\nn factorial<\/strong> the product of all the positive integers from 1 to [latex]n[\/latex]\r\n\r\nnth term of a sequence<\/strong> a formula for the general term of a sequence\r\n\r\nrecursive formula<\/strong> a formula that defines each term of a sequence using previous term(s)\r\n\r\nsequence<\/strong> a function whose domain is a subset of the positive integers\r\n\r\nterm<\/strong> a number in a sequence","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
explicit formula<\/strong> a formula that defines each term of a sequence in terms of its position in the sequence<\/p>\n
finite sequence<\/strong> 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]<\/p>\n
infinite sequence<\/strong> a function whose domain is the set of positive integers<\/p>\n
n factorial<\/strong> the product of all the positive integers from 1 to [latex]n[\/latex]<\/p>\n
nth term of a sequence<\/strong> a formula for the general term of a sequence<\/p>\n
recursive formula<\/strong> a formula that defines each term of a sequence using previous term(s)<\/p>\n
sequence<\/strong> a function whose domain is a subset of the positive integers<\/p>\n
term<\/strong> a number in a sequence<\/p>\n\n\t\t\t \n\t\t\t