Standard 11 : Sequences and Series (Archived)



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Define and use arithmetic and geometric sequences and series.

General Information

Number: MA.912.D.11
Title: Sequences and Series
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Discrete Mathematics

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.D.11.1: Define arithmetic and geometric sequences and series.
MA.912.D.11.2: Use sigma notation to describe series.
MA.912.D.11.3: Find specified terms of arithmetic and geometric sequences.
MA.912.D.11.4: Find partial sums of arithmetic and geometric series, and find sums of infinite convergent geometric series. Use Sigma notation where applicable.
MA.912.D.11.5: Explore and use other sequences found in nature such as the Fibonacci sequence and the golden ratio.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Tutorial

Name Description
The golden ratio:

In this tutorial, students learn an algebraic approach to understanding Phi, one of the most amazing numbers in mathematics.

Video/Audio/Animation

Name Description
MIT BLOSSOMS - Fabulous Fractals and Difference Equations :

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Virtual Manipulative

Name Description
Geometric and Harmonic Series- Limits:

This applet allows users to set up various geometric series with a visual representation of the successive terms, and the corresponding sum of those terms.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Tutorial

Title Description
The golden ratio:

In this tutorial, students learn an algebraic approach to understanding Phi, one of the most amazing numbers in mathematics.

Video/Audio/Animation

Title Description
MIT BLOSSOMS - Fabulous Fractals and Difference Equations :

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Virtual Manipulative

Title Description
Geometric and Harmonic Series- Limits:

This applet allows users to set up various geometric series with a visual representation of the successive terms, and the corresponding sum of those terms.