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What Are Number Sequences?

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, 2, 3, 4, 5, 6,,

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, 20, 30, 40, 50,

has the property that each number is 10 more than the previous one. You can therefore continue the sequence by thinking like this: 50 + 10 = 60 60 + 10 = 70 70 + 10 = 80

That gives you this pattern: Add 10. If you continue the sequence, the entire sequence up to 100 looks like this:

10, 20, 30, 40, 50, 60, 70, 80, 90, 100

10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Think About This

What are the next five even numbers?

2, 4, 6, 8, 10, 12,

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,

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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Examples of Mathematical Sequences