Arithmetic Sequences and Series

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Presentation transcript:

Arithmetic Sequences and Series Chapter 12-2 Dr. Guram Algebra II 2/25/16

Focus Questions How do we determine whether a given sequence is arithmetic? How do we find the common difference of an arithmetic sequence? How do we write an expression for an arithmetic sequence and calculate the nth term?

Curriculum standards HSF-BF.A.1 - Write a function that describes a relationship between two quantities. TN 3103.3.4 (Associated Tennessee Learning Expectations) Use the formulas for the general term and summation of finite arithmetic … series. Sources: http://www.corestandards.org/Math/Content/HSA/CED/A/1/ Spring Board Algebra 2 Textbook

Real World Examples Utilizing Arithmetic Series What are examples of ways people use arithmetic series in real world situations? ???

Real World Example of Arithmetic Series Thermostat: A room is 60 degrees and you feel cold. You increase it by 2 degrees to 62 degrees. You still feel cold, and increase it by 2 degrees, etc. Plant: You bought a plant at the store. It is currently 3 inches and grows 2 inches every month. How many inches will it be in 6 months?

Academic language Arithmetic Sequence: A sequence in which the difference of consecutive terms is constant. Common Difference: The constant difference of consecutive terms of an arithmetic sequence. Arithmetic Series: The expression formed by adding the terms of an arithmetic sequence.

Arithmetic Sequence Example 1

Arithmetic Sequence Example 1

Guided Practice Example

Arithmetic Sequence Key Concept

Example 2: Nth term

Example 2: Nth term

Arithmetic Sequence Example 3

Example 3 Answer

Example 3 Answer

Write a rule given two terms

Write a rule given two terms

Sum of a Finite Arithmetic Series

Standardized Test Practice

Standardized Test Practice

Arithmetic Sequence and Series in Real Life

Arithmetic Sequence and Series in Real Life

Review How do we determine whether a given sequence is arithmetic? How do we find the common difference of an arithmetic sequence? How do we write an expression for an arithmetic sequence and calculate the nth term?

Review of terms Explain the mathematical term: Arithmetic Sequence. Explain Arithmetic Series. Give a real world example of Arithmetic Sequence/Series.

Class and HW Problems 12.2 Worksheet