1. **Stating the problem:** We are given a sequence of equations: $$1 + 1 = 20$$ $$2 + 2 = 80$$ $$3 + 3 = 180$$ $$4 + 4 = ?$$ We need to find the pattern and determine the value of $$4 + 4$$ in this sequence. 2. **Analyzing the pattern:** Let's look at the left side and the right side of each equation: - For $$1 + 1$$, the result is $$20$$. - For $$2 + 2$$, the result is $$80$$. - For $$3 + 3$$, the result is $$180$$. 3. **Finding a formula:** Notice that the left side sums are $$2, 4, 6$$ respectively. Let's check if the right side relates to the sum squared times some factor: - $$1 + 1 = 2$$, and $$20 = 2^2 \times 5 = 4 \times 5$$ - $$2 + 2 = 4$$, and $$80 = 4^2 \times 5 = 16 \times 5$$ - $$3 + 3 = 6$$, and $$180 = 6^2 \times 5 = 36 \times 5$$ So the pattern is: $$\text{Result} = (\text{Sum})^2 \times 5$$ 4. **Applying the formula to $$4 + 4$$:** - Sum: $$4 + 4 = 8$$ - Result: $$8^2 \times 5 = 64 \times 5 = 320$$ 5. **Final answer:** $$4 + 4 = 320$$