# 8.1 – Finding Patterns

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.

• 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, … $y=2x-1$
• 1, 3, 9, 27, 81, 243 … $y=3^x$

• 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

• 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.