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# Arithmetic Sequences

Lesson 4 of 18

## Objective: SWBAT find partial sums for arithmetic sequences and use them to solve problems.

*50 minutes*

#### Launch and Explore

*20 min*

We have been doing some introductory work with sequences and series, but today we are going to focus solely on arithmetic sequences. I tried to **up the ante with these problems** by pressing my students to fully realize the meaning of *S _{n}= *(

*n*/2)(

*a*

_{1 }+

*a*) and

_{n}*a*=

_{n}*a*

_{1}+

*d*(

*n*– 1). We have done enough conceptual work that I think these formulas will make sense to students. I also give them a few questions where they need to find something that was given in the previous lessons. For example, finding the common difference of a sequence is you know two partial sums.

I begin today's class by giving students this worksheet and giving them 15-20 minutes to work on it with their table groups. In this video I discuss some of the things I will be looking out for as students are working collaboratively.

*expand content*

#### Share

*15 min*

After students have ample time to investigate these sequence problems, I want to have a **group discussion** about them. As I am moving around the classroom I will see if there is a need to go through Questions #1 and #2. Usually the majority of the class understands the method and I will clear up minor issues if I see them.

For Question #3 through #5, I will choose a student to present their work using the document camera. As discussed in my video, **question #3 is important** because I don’t want students to over generalize the formula for the *n*th partial sum of an arithmetic sequence and think that it will work for any sequence. I will make sure that students understand this and elicit multiple explanations for that question.

#### Resources

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#### Summarize and Extend

*15 min*

Here is an assignment for students to cement their knowledge of arithmetic sequences and series.

**Teacher Note:** the first question on the worksheet has some problems from our textbook. You will have to change these to reflect your textbook or you may omit them.

#### Resources

*expand content*

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
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- UNIT 8: Matrices and Systems
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- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: The Skyscraper Problem
- LESSON 2: The Fractal Tree
- LESSON 3: Describing Sequences and Series
- LESSON 4: Arithmetic Sequences
- LESSON 5: Geometric Sequences
- LESSON 6: The Fractal Tree Revisited
- LESSON 7: Investments, Loans, and Mortgages - Day 1 of 2
- LESSON 8: Investments, Loans, and Mortgages - Day 2 of 2
- LESSON 9: Mathematical Induction
- LESSON 10: Formative Assessment Review: Sequences and Series
- LESSON 11: Formative Assessment: Sequences and Series
- LESSON 12: The Limit of a Sequence
- LESSON 13: Area Under a Curve - Day 1 of 2
- LESSON 14: Area Under a Curve - Day 2 of 2
- LESSON 15: Binomial Expansion
- LESSON 16: Unit Review: Sequences and Series
- LESSON 17: Unit Review Game: Pictionary
- LESSON 18: Unit Assessment: Sequences and Series