**Objectives**

- Identify real-world patterns that repeat themselves.
- Find the missing term in a pattern of pictures, letters, or numbers.

**Key Terms**

- Pattern – A consistent or characteristic form, style, or method used to connect various objects or ideas.

Ex. 2, 6, 18, 54, …

**Notes**

- When you look for a pattern, you are searching for repeating colors, shapes, words, letters, or numbers.

- Questions to Ask Yourself About a Pattern
- Is a certain number added or subtracted at each step to get the next number?
- Is each number multiplied or divided by a certain number?
- Are different numbers, which themselves form a pattern, added to each number?
- Are a few of the above cases happening?

- Sometimes a list of numbers forms a sequence that can be described by an algebraic function.
- 1, 3, 5, 7, …
- 1, 3, 9, 27, 81, 243 …

- Finding the pattern often starts with looking for a rule that will explain how you get from one term in the list to the next.
- 1, 3, 5, 7, … add 2 each step
- 1, 3, 9, 27, 81, 243, … multiply by 3 each step

- Example: Which number is the next number in the following pattern?
- 2, -3, 4, -5, _____
- Pattern: + – + – … and numbers increase by 1
- Answer: 6

- Sierpinski Triangle Patterns

- Money Investment Patterns
- You won $1 Million dollars and plan to invest the money. Would you have more money if you took the $1 Million up front or received $50,000 each year for 20 years?
- If you invest the $1 Million up front, your money could grow with interest over the next 20 years; so, you would end up having more money this way!
- If you only invest $50,000 each year, your money won’t grow as fast, as the interest base is much less than $1 Million.
- Remember: investments that compound have exponential growth!
- Exponential growth is a geometric sequence.

- You won $1 Million dollars and plan to invest the money. Would you have more money if you took the $1 Million up front or received $50,000 each year for 20 years?