Section 03 — Patterns & Sequences

Course: LBS 110 – Mathematics for Modern Thinkers

Learning Session

Explore These Materials: 1. Read (45 min) — Intro to sequences: arithmetic vs geometric; Fibonacci and the idea of recurrence (short notes).
2. Watch (60 min) — Visual Patterns in Nature (morphogenesis); Numberphile‑style segment on famous integer sequences.
3. Listen (30 min) — A short piece on pattern recognition and perception.
4. Reflect While Engaging — Log where you see repeating structure today (music, architecture, calendars, code, exercise sets).

Key Quote Box

“_____________”

Practice

1. Daily Sequence — Record an activity as an arithmetic sequence (e.g., steps, reps, minutes). Graph it.
2. Growth Patterns — Model a simple geometric growth (e.g., savings with constant percentage); explain parameters.
3. Recurrence Sketch — Define a recurrence for a simple process (e.g., cooling coffee, stairs workout) and compute first 10 terms.
4. Pattern Hunt — Photograph or sketch 3 natural or human‑made patterns; annotate the rule you suspect.
5. Reflection — What’s the difference between a pattern I impose vs one I discover?

Hard Problem (Optional)

Given a recurrence aₙ = 2·aₙ₋₁ + 1 with a₀ = 0, find a closed form for aₙ and justify it informally.