First off, this idea is in no way unique to me. The ideas that love to use in class are typically ones that I "steal" from other teachers.
I am starting to cover sequences in my algebra course. Students typically catch on quickly and I try to stay away from drill and kill type practice especially for problems like sequences. A great way for students to get practice of procedural concepts in a "fun" way is Math BINGO. I give each student a sheet at the beginning of class and place 16 numbers they use to fill in each square. After we go over a problem or two (where they will find the first 6 terms of the sequence) I turn to this game. I pass out beans or BINGO markers and we play.
When I call out the sequence I will write the rule of sequence on the board and speak what nth term I want them to find. By verbalizing that part, my students have to be able to understand the vocabulary used to correctly answer the question. And any opportunity I can use for them to follow directions is a plus!
To make it last longer I will set a certain rule. For example, to BINGO the student will have to have 2 columns filled or 1 column and 1 row filled. I will usually play one more "sequence rule" after someone has won. (They always beg for another round though...be ready for that!)
It's quick, it's easy to understand, and it shakes up the ordinary. It also can be edited to fit any topic. I used this with my Math 3 Support students to review solving expressions with logs and natural logs. The possibilities are endless!
The file below is of the cards I use. Each page has 4 cards. If you want this to last the entire class, I would double side it so each student could have 2 cards with 2 different set of numbers of each side.
Educator who loves math and working with students.