Investigating Infinite Geometric Series

Objective

Students will be able to dive into a study of the uniqueness of convergence of infinite geometric series.

Big Idea

The last several lessons have been highly practical and focused on real world application. This lesson further emphasizes mathematical questioning associated with behavior of infinite geometric series.

Lesson Author

Jarod Hammel

Huntington, IN

Grade Level

Eleventh grade

Subjects

Math

Number Sense and Operations

Algebra

Patterns (Algebra)

Standards

HSA-SSE.B.4

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.★

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-BF.A.1

Write a function that describes a relationship between two quantities.*

HSF-BF.A.2

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*

HSF-LE.A.2

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP5

Use appropriate tools strategically.

MP8

Look for and express regularity in repeated reasoning.