# Spot the pattern A sequence: `3, 6, 9, 12, …` Each term adds 3. That is a **rule**. Another: `2, 4, 8, 16, …` — multiply by 2 each time. ## Ask 1. What do I do to get the next term? 2. Does the same rule work every step? ## Term number Position 1, 2, 3, 4, … We often call the position `n`. For 3, 6, 9, 12: the n-th term looks like `3n` (n=1 → 3, n=2 → 6, …) > Patterns are algebra’s playground. The letter n is just “which place in the line”. ## Two questions, every sequence 1. What happens from term to term? 2. Does that exact thing happen on **every** jump shown? If yes, you have a rule. If no, try a different idea (maybe multiply, maybe subtract). ### Term number The first term is position `n = 1`, not n = 0, unless a question says otherwise at this level. For 3, 6, 9, 12 the n-th term is `3n` because seat 1 holds 3, seat 2 holds 6, … ### Patterns are algebra The letter n is just “which place”. That is the same mystery-box idea as x, used for position.