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Sequences are a lot of fun. Even numbers and odd numbers are examples of sequences that follow a special pattern. In the boxes below you can try to continue a couple of sequences yourself.

But what is a sequence, really? A sequence is just a row of numbers that aren’t jumbled together, which means the numbers in the sequence follow a specific pattern.

Example 1

The positive integers:

$$1,\phantom{\rule{7.92491pt}{0ex}}2,\phantom{\rule{7.92491pt}{0ex}}3,\phantom{\rule{7.92491pt}{0ex}}4,\phantom{\rule{7.92491pt}{0ex}}5,\phantom{\rule{7.92491pt}{0ex}}6,\dots ,$$ |

are an example of a sequence with a pattern. You get the next number in the sequence by adding $1$ to the previous number. That gives us this pattern: Add $1$.

Example 2

The sequence

$$10,\phantom{\rule{7.92491pt}{0ex}}20,\phantom{\rule{7.92491pt}{0ex}}30,\phantom{\rule{7.92491pt}{0ex}}40,\phantom{\rule{7.92491pt}{0ex}}50,\dots $$ |

has the property that each number is $10$ more than the previous one. You can therefore continue the sequence by thinking like this:

$$\begin{array}{llll}\hfill 50+10& =60\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 60+10& =70\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 70+10& =80\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$That gives you this pattern: Add $10$. If you continue the sequence, the entire sequence up to $100$ looks like this:

$$\begin{array}{llll}\hfill & 10,\phantom{\rule{7.92491pt}{0ex}}20,\phantom{\rule{7.92491pt}{0ex}}30,\phantom{\rule{7.92491pt}{0ex}}40,\phantom{\rule{7.92491pt}{0ex}}50,\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & 60,\phantom{\rule{7.92491pt}{0ex}}70,\phantom{\rule{7.92491pt}{0ex}}80,\phantom{\rule{7.92491pt}{0ex}}90,\phantom{\rule{7.92491pt}{0ex}}100\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

$$10,\phantom{\rule{7.92491pt}{0ex}}20,\phantom{\rule{7.92491pt}{0ex}}30,\phantom{\rule{7.92491pt}{0ex}}40,\phantom{\rule{7.92491pt}{0ex}}50,\phantom{\rule{7.92491pt}{0ex}}60,\phantom{\rule{7.92491pt}{0ex}}70,\phantom{\rule{7.92491pt}{0ex}}80,\phantom{\rule{7.92491pt}{0ex}}90,\phantom{\rule{7.92491pt}{0ex}}100$$ |

Think About This

**What are the next five even numbers? **

$$2,4,6,8,10,12,\dots $$ |

You can see that you have to skip a number to get to the next even number. That means you skip $13$ and go straight to $14$, which is an even number. Likewise, you skip $15$ and get the even number $16$, skip $17$ and get the even number $18$, and skip $19$ to get the even number $20$. Finally, you skip $21$ and get the even number $22$.

That means the next five even numbers are

$$14,16,18,20,22.$$ |

The sequences become slightly more challenging and interesting the more you learn, so use some time to understand how this works. Later on, you’ll learn how to do calculations on different kinds of sequences and see how they’re used in daily life.

Think About This

**What are the next five odd numbers? **

$$1,3,5,7,9,11,\dots $$ |

You see that you have to skip a number to get the next odd number. That means you skip $12$ to get the odd number $13$. Likewise, you skip $14$ to get the odd number $15$, skip $16$ to get the odd number $17$, and skip $18$ to get the odd number $19$. Finally, you skip $20$ to get the odd number $21$.

That means the next five odd number are

$$13,15,17,19,21.$$ |

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