🎓 Deeper Dive — Adults

A sequence with a rule is a pattern. Arithmetic progression (AP): add a constant d (e.g. 3, 7, 11, 15 → d=4). Geometric progression (GP): multiply by r (e.g. 2, 6, 18, 54 → r=3).

Fibonacci: each term = sum of previous two (1, 1, 2, 3, 5, 8, 13). The ratio of consecutive terms approaches the golden ratio φ ≈ 1.618.

Patterns underpin coding (loops), recursion, and predictive AI.