# Number pattern

A number pattern is a series of numbers arranged or repeated in some order or design. Number patterns are also referred to as number sequences. In algebra there are many different types of sequences, such as arithmetic sequences, geometric sequences, and more. Some of the patterns discussed below may fall into those categories, but for now we will just discuss number patterns in a broad sense.

### Pattern of odd numbers

An example of a pattern of odd numbers is one that includes all positive odd numbers:

1, 3, 5, 7, 9, 11, ...

In the above example, the "..." indicates that the pattern continues all the way to infinity. This is a simple pattern that includes all the positive odd numbers.

Example

Determine the number pattern for the following set of numbers:

1, 5, 9, 13, 17, 21, 25...

The above number pattern is a pattern of every other odd number. We skip one odd number between each, which effectively means that we are adding 4 to the preceding value to find the subsequent value.

Similar patterns can also be observed in even numbers.

### Pattern of multiples of a number

In a number pattern involving multiples, each subsequent value is related to the previous value by some multiple. The following is a number pattern involving multiples of 3.

0, 3, 6, 9, 12, 15, ...

In the above example, we can see that each subsequent number is the next multiple of 3, starting from 3 × 0 = 0, and proceeding through 3 × 1 = 3, 3 × 2 = 6, 3 × 3 = 9, and so on through infinity. We can also look at this as an example of skip counting, where we are counting by 3s, starting from 0. Below is a table in which the multiples of 3 are filled in. A table containing the numbers 1-100 can be a useful way to visualize what various number patterns look like.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |

61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |

71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

### Pattern of powers

In a pattern of powers, subsequent values in the pattern are related to the previous value by some power. Below is a number pattern involving powers of 2.

2, 4, 8, 16, 32, 64, ...

Each subsequent value is the following power of 2, starting with 2^{1} = 2, and progressing through 2^{2} = 4, 2^{3} = 8, 2^{4} = 16, and so on.

Example

Determine the number pattern for the follwoing set of numbers.

4, 16, 64, 256, 1024, ...

The above number pattern is still related to powers of 2, except that rather than raising 2 to the power of n, where n represents which number in the pattern we are referring to, we raise 2 to the power of 2n:

2^{(2 × 1)} = 4

2^{(2 × 2)} = 16

2^{(2 × 3)} = 64

2^{(2 × 4)} = 256

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The ability to recognize number patterns is part of number sense, a skill that we need to practice to improve our mathematical ability. There are many things in everyday life, as well as in the study of mathematics, that exhibit number patterns. One such example is the Fibonacci sequence, which we see frequently in many applications.

### Fibonacci sequence

The Fibonacci sequence is a number pattern that appears in many aspects of mathematics, such as the golden ratio, the way in which the branches of trees grow, the arrangement of leaves on a plant's stem, and more. The Fibonacci sequence is as follows:

0, 1, 1, 2, 3, 5, 8, 13, ...

In the Fibonacci sequence, each subsequent value is the result of adding the previous 2 values, starting from 0 and 1.

### Did you know?

The Fibonacci sequence is named for an Italian mathematician named Leonardo Fibonacci, who lived about 800 years ago.

This sequence can be found in many living things, such as the pine cone. If you count the seeds in the spirals of the pine cone, you will find adjacent numbers in the Fibonacci sequence.