Recursion & Sequences
📋 What it is
RECURSION defines something in terms of itself — each step built from the previous ones.
🗣️ Coach says
A recursive rule says "to get the next term, use the ones before it". The Fibonacci sequence adds the last two: 1, 1, 2, 3, 5, 8, 13… Recursion is how you fold a big problem into a smaller copy of itself, and it is everywhere in nature and in code — even a folder that contains folders.
🧠 Memory hook
Recursion = defined by itself. Fibonacci: next = sum of the previous two (…5, 8, 13…).
😂 Giggle
What did the permutation say to the combination?
"Order matters to me, but I see it doesn't bother you!"
😲 Whoa!
Fibonacci numbers show up in sunflower seeds, pinecones, and spiral shells — nature counts recursively.
✅ Quick check: The Fibonacci sequence is 1, 1, 2, 3, 5, 8, … What comes next?
Say your answer out loud first — then reveal.
13 (8 + 5).
Each Fibonacci term is the sum of the two before it: 8 + 5 = 13.
🧪 Try it! (2 minutes)
Write the first 8 Fibonacci numbers by always adding the last two. Predict each before you add.