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Sep18

# Variety of Series and Patterns in Math

What is a series? And a pattern? In this post, we’ll teach you all about series and patterns.

Regularities are everywhere and it’s a special skill to be able to recognize them. Regularities exist in natural and social phenomena; the search for regularities is the base of science.

Just by observing your surroundings, you can find groups of elements that have been set in a certain way that follow a rule. You can find patterns!

### What exactly are series and patterns?

A pattern is a succession of elements (they could be auditory, gestural, graphic…) that is formed by following a rule; that rule can be either repetition or reoccurrence.

#### Repeating Patterns:

Repeating patterns have different elements that are displayed periodically.

We can make lots of diverse repeating patterns, keeping its structure in mind. Here are some examples:

• AB: Two different alternated elements are repeated.

• ABC: Three different alternated elements are repeated.

• AAB: One element is repeated two times and followed by another.

• AABB: One element is repeated two times and followed by two repetitions of another.

#### Reoccurring Patterns:

In reoccurring patterns, the elements change with regularity. We can infer the rule of its formation; that’s to say, you can find out what the next element will be by observing how the pattern of the revealed elements. For example:

Now that we know what a pattern is and the types of rules that they can follow, we’re going to take a look at some pattern and series activities:

There are exercises where we can only copy a given pattern (reproduction):

In others, we’ll have to identify the pattern that a series is following (identification):

While there are others where we need to identify the pattern that we need in order to continue a series (extension):

And there are even exercises where we need to identify the pattern to be able to complete a series (extrapolation):

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