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Study Guides > College Algebra

Key Concepts & Glossary

Key Equations

Formula for a factorial 0!=11!=1n!=n(n1)(n2)(2)(1), for n2\begin{array}{l}0!=1\\ 1!=1\\ n!=n\left(n - 1\right)\left(n - 2\right)\cdots \left(2\right)\left(1\right)\text{, for }n\ge 2\end{array}

Key Concepts

  • A sequence is a list of numbers, called terms, written in a specific order.
  • Explicit formulas define each term of a sequence using the position of the term.
  • An explicit formula for the nthn\text{th} term of a sequence can be written by analyzing the pattern of several terms.
  • Recursive formulas define each term of a sequence using previous terms.
  • Recursive formulas must state the initial term, or terms, of a sequence.
  • A set of terms can be written by using a recursive formula.
  • A factorial is a mathematical operation that can be defined recursively.
  • The factorial of nn is the product of all integers from 1 to nn

Glossary

explicit formula
a formula that defines each term of a sequence in terms of its position in the sequence
finite sequence
a function whose domain consists of a finite subset of the positive integers {1,2,n}\left\{1,2,\dots n\right\} for some positive integer nn
infinite sequence
a function whose domain is the set of positive integers
n factorial
the product of all the positive integers from 1 to nn
nth term of a sequence
a formula for the general term of a sequence
recursive formula
a formula that defines each term of a sequence using previous term(s)
sequence
a function whose domain is a subset of the positive integers
term
a number in a sequence
 

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