I start class by asking students what strategies they use to determine if a sequence is arithmetic or geometric. I am looking for students to clearly distinguish between the two kinds of sequences and for them to articulate how to find the constant difference or constant ratio. Next, I ask students what strategies they have for writing recursive equations and we do the same for explicit equations. I might spend a little more time eliciting ideas for explicit equations for geometric sequences because I know this is where students really struggle.
We read through the instructions for the sequences assessment together. I make sure students understand that the top line of each function asks them to describe how to find the next term (this should also be helpful for them to write the recursive function). I also remind students that they have a model example to work with.
I scale the difficulty of these problems based on the students in my class. If you are working with more advanced students, you could include a lot more sequences that involve fractions or decimals or a have a negative constant ratio.
The sequences assessment is derived from What Comes Next, What Comes Later?
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