# Arithmetic Sequences

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## Objective

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

#### Big Idea

Formalize arithmetic sequences by moving to formulas.

## Launch and Explore

20 minutes

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 Sn= (n/2)(a1 + an) and an= a1+ 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.

## Share

15 minutes

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 nth 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.

## Summarize and Extend

15 minutes

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.