A **number pattern** is a list of numbers which follow a rule.

To find the first four numbers of pattern X, start with 0, then add 1 three times.

| starting number |
add 1 to 0 |
add 1 to 1 |
add 1 to 2 |

PATTERN X |
0 | 1 | 2 | 3 |

To find the first four numbers of pattern Y, start with 0, then add 3 three times.

| starting number |
add 3 to 0 |
add 3 to 3 |
add 3 to 6 |

PATTERN Y |
0 | 3 | 6 | 9 |

One observation is that the terms of pattern Y are three times the corresponding terms of pattern X.

PATTERN X TERMS × 3 | 0 × 3 |
1 × 3 |
2 × 3 |
3 × 3 |

0 | 3 | 6 | 9 |

Another observation can be made about the difference between corresponding terms of patterns X and Y.

DIFFERENCE BETWEEN TERMS | 0 - 0 |
3 - 1 |
6 - 2 |
9 - 3 |

0 | 2 | 4 | 6 |

Notice the difference between corresponding terms of the patterns results in a pattern with a rule of *add 2*.