Creating Equations for Exponential Growth: Geometric Sequences

This lesson teaches how to create an equation for a geometric sequence using tables and graphs. It reviews exponential functions, explains the initial value and common ratio in geometric sequences, and highlights common student mistakes. A practical example with paper tearing demonstrates the concept, and the lesson concludes with graphing the sequence to visualize the pattern.

What is the common ratio in a geometric sequence where each term is multiplied by 3?

• 2

• 1

• 4

• 3

Which of the following is a common mistake when working with geometric sequences?

• Ignoring the initial value

• Forgetting to square the terms

• Using addition instead of multiplication

• Confusing the initial value with the common ratio

If you start with one piece of paper and tear it in half repeatedly, what is the common ratio of the sequence?

• 1

• 2

• 3

• 4

How many pieces of paper will you have after 10 tears if you start with one piece and double it each time?

• 2048

• 1024

• 512

• 256

What type of graph represents the number of pieces of paper after each tear?

• Exponential

• Logarithmic

• Linear

• Quadratic