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Arithmetic Sequences
An Arithmetic Sequence is made by adding whatever value for individually one time.
Examples:
|1, 4, 7, 10, 13, 16, 19, 22, 25, |
|... |

This sequence has a divergence of 3 between each play.
The chemical formula is move by adding 3 to the fail number each time.

|3, 8, 13, 18, 23, 28, 33, 38, |
|... |

This sequence has a exit of 5 between each number.
The pattern is continued by adding 5 to the last number each time.
The value added each time is called the common difference
What is the common difference in this example?
|19, 27, 35, 43, |
|... |

Answer: The common difference is 8
The common difference could also be negative, like this:
|25, 23, 21, 19, 17, 15, ...|

This common difference is -2
The pattern is continued by subtracting 2 each time.
 
Geometric Sequences
A Geometric Sequence is made by multiplying by most value each time.
Examples:
|2, 4, 8, 16, 32, 64, 128, 256, |
|... |

This sequence has a factor of 2 between each number.
The pattern is continued by multiplying the last number by 2 each time.
|3, 9, 27, 81, 243, 729, 2187, ...|

This sequence has a factor of 3 between each number.
The pattern is continued by multiplying the last number by 3 each time.




 
Special Sequences
Triangular Numbers
|1, 3, 6, 10, 15, 21, 28, 36, 45, |
|... |

This Triangular Number Sequence is generated from a pattern of dots which form a triangle.
By adding another course of study of dots and counting all the dots we can find the next number of the sequence:
[pic]
Square Numbers
|1, 4, 9, 16, 25, 36, 49, 64, 81, |
|... |

The next number is made by squaring where it is in the pattern.
The second number is 2 squared (22 or 2×2)
The seventh number is 7 squared (72 or 7×7) etc
Cube Numbers
|1, 8, 27, 64, 125, 216, 343, 512, 729, ... |

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