We have seen number patterns in sequences.
Now, we will take a look at patterns involving "objects" as the terms of the sequence.

Working with objects in sequences may be called pattern recognition or abstract reasoning.

definition
A pattern is a group of numbers or objects that follow a rule as the pattern is extended.

A list of terms that form a pattern is referred to as a sequence.

Examples of Patterns with Objects:

When working with objects, look for changes in the object itself, changes between the objects, and/or transformations of the object. Consider the following sequences and their patterns:
Sequence Pattern
9pattern
The triangles are growing by one "row" of blue circles each time. The number of circles comprising the triangles is 1, 3, 6, 10, 15, where the number of circles in the new row is added each time: 2, 3, 4, 5,...
The next triangle will have 21 circles (15 + 6 from a new row).
99pattern
The figures appear to be regular polygons. Each figure has one more side than the previous figure. The next figure is a septagon (7 sides).
boxpattern
This pattern has no numeric connection. The black circle is moving clockwise around the grid. the next term will be the same as the first.
diepattern
Two patterns exist between every other die. The first, third, fifth, (etc.) die is each 6. while the second, fourth, sixth, (etc.) die is a counting number starting with 1.
6, 1, 6, 2, 6, 3, ... next die will be 6.
ARROWCIRCLE
The figure is rotating counter- clockwise by 90ยบ each time. The next figure will be the same as the first figure.




Examples of Patterns with Letters:


Sequences may contain letters. Consider how the pattern is developing, and/or what you know about the locations of the letters in the alphabet.

Sequence Pattern
a, c, e, g, i, k, m, ...
The pattern is every other letter of the alphabet starting with a. The next letter is o.
a, z, b, y, c, x, d, ...
The letters are alternating with letters starting with a and moving forward, and letters starting at z and moving backward. a, z, b, y, c, x, d,... The next letter is w.
b, e, h, k, n, q, ...
Starting with the letter b, this pattern is every third following letter. The next letter will be t.
m, n, o, m, n, o, m, ...
There is a repetition in this pattern of the letters m, n, o.
The next letter will be n.
b, g, d, i, f, k, ...
Determining this pattern requires looking at the position of the letters in the alphabet.
b, g, d, i, f, k = 2, 7, 4, 9, 6, 11.
The red values are even numbers (every other term).
The black values are 5 more than their preceding even values. The next term is h which is 8.

As you work with sequences, you will be exposed to more types of patterns.
The more patterns you see, the easier it will be to decipher new patterns.


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