# Finding the Rule for an Arithmetic Sequence by Graphing Foldable

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I created this foldable to teach finding the rule for an arithmetic sequence by graphing to my Algebra 1 students.

As I posted before, this is my first year teaching sequences in Algebra 1.  The new Oklahoma math standards (OAS) include this standard:

A1.A.3.5 Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Use the pattern, find the next term.

After going over the difference between arithmetic and geometric sequences, we completed this finding the rule for an arithmetic sequence by graphing foldable in our Algebra 1 interactive notebooks.

For each sequence, students had to create a graph.  They used this graph to find the slope and determine what the y-intercept of the function would be.

My students were a bit confused at first when it came to how to graph the sequence on the coordinate plane.  Many students thought that our first point should be graphed on the y-axis.  Now that I think about it, having students make a table with “Term” and “Value” as the two columns would have taken care of this because it would have turned the sequence into a set of ordered pairs.  I will definitely add a table to these notes for next year!

We examined the graphed points to find the slope of the line.  This value went in front of x.  Then, we used the slope to determine where the line would cross the y-axis.  This gave us the rest of our rule.

After doing a couple of these together, many of my students were working ahead without any prompting from me.

I loved how we derived the formula for arithmetic sequences by noticing that it made a linear function.  It flowed so nicely in class due to the fact that we had spent so much time focusing on linear functions earlier in the year.

My students would probably have been perfectly happy to make graphs in order to find the rule, but I decided to show them a method of finding the rule that doesn’t require making a graph.

## Alternate Version of Foldable with Tables

In 2018, I updated this foldable to include tables for my students to fill out to help them organize their work. It went much smoother this way!

## More Activities for Teaching Sequences and Series

• The Splice is Right Puzzle
• Step Puzzles by Naoki Inaba – A Logic Puzzle for Introducing Arithmetic Sequences