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.
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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.
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.