S2
Iteration & Repetition
Iteration → Recursion
"If you can repeat, you can predict."
Philosophical Origin：Euclidean algorithm
Minimal Example
Addition: 2+2+2+2+2 = 5×2. Multiplication is repeated addition. Extend: 2,4,6,8,10 is an arithmetic sequence.
One-Line Rule
"Repetition is the seed of patterns."
Common Misconception vs Correct Understanding
Sequences must be memorized.
Sequences are results of repetition.
🌱 Growth Steps (Natural Evolution)
1 / 5 步
1
Repeated addition → Multiplication
✨ Starting Point: Growth begins here
如果你能 ↑ 那么你就能 ↓
2
Repeated subtraction → Division
如果你能 ↑ 那么你就能 ↓
3
Constant difference → Arithmetic sequence
如果你能 ↑ 那么你就能 ↓
4
Constant ratio → Geometric sequence
如果你能 ↑ 那么你就能 ↓
5
From repetition to pattern → Recursion and closed form
SAT Example Question
Question:
What is the 50th term of the sequence 3,7,11,15,...?
Answer:
199
Explanation:
Arithmetic, d=4, a₅₀ = 3 + (50-1)×4 = 199
Practice Questions
5 questions with multiple solution methods
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