A sequence is a list with structure. Recursion is what happens when each term knows something about the previous terms.
Students usually meet sequences as formulas. COSMO lessons work better when they meet them as patterns first.
Two Ways to Describe a Sequence
An explicit formula tells you the nth term directly.
A recursive rule tells you how to get the next term from earlier terms.
Both are useful, but they answer different questions.
Activity
Give students this sequence:
1, 1, 2, 3, 5, 8, 13, …
Ask them to predict the next terms, then write a rule. Only after that should you name it as recursive.
Challenge
Create a recursive sequence that grows slowly at first and then suddenly becomes large.