Good news: you've actually been working with algebra since you were three and began to notice patterns (red dog, blue cat, red dog, blue cat…). The patterns we're going to work with now are just a little more complex and may take more brain power. Patterns are the beginning of algebra.
There are endless types of patterns and methods for solving patterns. We've mostly been working with simple arithmetic (patterns involving adding or subtracting a number each time) or geometric patterns (ones involving multiplying or dividing by a number).
Here are three common types of patterns we've seen.
| Type | Example | Solution |
|---|---|---|
| Arithmetic | 1, 3, 5, 7, 9... | Add 2 each time. |
| 99, 90, 81, 72... | Subtract 9 each time | |
| Geometric | 1, 2, 4, 8, 16... | Multiply the previous number by 2. |
| 1000, 100, 10, 1... | Divide the previous number by 10. | |
| Geometric - Exponential | 2, 4, 16, 256... | Square the previous number. |
| 1, 4, 9, 16, 25... | 12, 22, 32, 42, 52... |
Look Out: an exponential pattern is actually a type of geometric pattern. However, to help explain things, we made them a subcategory.
Here's a video example of math in action. Just a sample of questions you might see.
Example 1
The first four triangle numbers are 1, 3, 6, and 10. They are called triangular because they can be arranged in dots as triangles, like so:
What will the 10th triangular number be? |
Example 2
Find the next two numbers in this pattern: 1, 2, 8, 48, 384… |
Example 3
Find the missing number in the pattern: 3, 9, 81, ___, 43,046,721. |
