1. **Problem:** Explain the Fibonacci sequence and draw a picture using the sequence. 2. **What the Fibonacci sequence is:** The Fibonacci sequence is a list of numbers where each new number is found by adding the two numbers before it. 3. **Formula/rule:** If the sequence is $F_1, F_2, F_3, \dots$, then the rule is $$F_n = F_{n-1} + F_{n-2}$$ for $n \ge 3$. The usual starting values are $$F_1 = 1, \quad F_2 = 1.$$ 4. **Build the sequence step by step:** $$1,\ 1,\ 2,\ 3,\ 5,\ 8,\ 13,\ 21,\ \dots$$ Here is how the early terms are made: - $1$ and $1$ are the starting numbers. - $1 + 1 = 2$ - $1 + 2 = 3$ - $2 + 3 = 5$ - $3 + 5 = 8$ - $5 + 8 = 13$ 5. **Important rule to remember:** Each term is the sum of the two terms right before it. That means the sequence keeps growing because you are always adding positive numbers. 6. **Picture using the sequence:** A common picture for the Fibonacci sequence is a set of squares whose side lengths match the numbers in the sequence. This makes a spiral-like pattern when you connect them. 7. **Final answer:** The Fibonacci sequence starts as $1, 1, 2, 3, 5, 8, 13, 21, \dots$ and follows $F_n = F_{n-1} + F_{n-2}$.