1. **State the problem:** We want to find the number of tiles in the 100th pattern of a sequence where the number of tiles in each pattern is given by the formula: $$\text{number of tiles} = 4 \times \text{pattern number} + 7$$ 2. **Understand the formula:** The formula means for any pattern number $n$, the number of tiles is $4n + 7$. 3. **Apply the formula for the 100th pattern:** Substitute $n = 100$ into the formula: $$\text{number of tiles} = 4 \times 100 + 7$$ 4. **Calculate:** $$4 \times 100 = 400$$ So, $$\text{number of tiles} = 400 + 7 = 407$$ 5. **Final answer:** The 100th pattern has **407 tiles**.