# 7.2: Explicit Formulas

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**Practice**Explicit Formulas

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Color | Highlighted Text | Notes | |
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Term | Definition |
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arithmetic sequence |
An arithmetic sequence has a common difference between each two consecutive terms. Arithmetic sequences are also known are arithmetic progressions. |

common difference |
Every arithmetic sequence has a common or constant difference between consecutive terms. For example: In the sequence 5, 8, 11, 14..., the common difference is "3". |

common ratio |
Every geometric sequence has a common ratio, or a constant ratio between consecutive terms. For example in the sequence 2, 6, 18, 54..., the common ratio is 3. |

Explicit |
Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms. |

Explicit formula |
Explicit formulas define each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms. |

geometric sequence |
A geometric sequence is a sequence with a constant ratio between successive terms. Geometric sequences are also known as geometric progressions. |

index |
The index of a term in a sequence is the term’s “place” in the sequence. |

Natural Numbers |
The natural numbers are the counting numbers and consist of all positive, whole numbers. The natural numbers are the numbers in the list 1, 2, 3... and are often referred to as positive integers. |

recursive |
The recursive formula for a sequence allows you to find the value of the n^{th} term in the sequence if you know the value of the (n-1)^{th} term in the sequence. |

recursive formula |
The recursive formula for a sequence allows you to find the value of the n^{th} term in the sequence if you know the value of the (n-1)^{th} term in the sequence. |

sequence |
A sequence is an ordered list of numbers or objects. |

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Description

Explicit formulas for identifying terms of a sequence without knowing the preceding term.

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At Grade
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Date Created:

Nov 01, 2012
Last Modified:

Mar 23, 2016
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