The Ohio Journal of School Mathematics has just posted a newly published article, What Are The Next Three Terms In This Sequence?, by Janet Walker and Matthew McBurney of Indiana University of Pennsylvania.
Here's a link: https://library.osu.edu/ojs/index.php/OJSM/article/view/5816. The authors explore a task that---on its surface---appears unremarkable. However, upon closer inspection (and with the help of some algebra and technology) yields some cool mathematics. Arguably more importantly, they illustrate the danger of assuming that routine tasks have only one solution.
I love their use of TI-Nspire and the Online Encyclopedia of Integer Sequences (OEIS). You really must check out their paper! :)