1. The problem is to evaluate the sum $$\sum_{x=1}^5 (-1)^x 3^x$$. 2. The formula for the sum of terms is given by adding each term from $x=1$ to $x=5$: $$\sum_{x=1}^5 (-1)^x 3^x = (-1)^1 3^1 + (-1)^2 3^2 + (-1)^3 3^3 + (-1)^4 3^4 + (-1)^5 3^5$$ 3. Calculate each term: - For $x=1$: $(-1)^1 3^1 = -1 \times 3 = -3$ - For $x=2$: $(-1)^2 3^2 = 1 \times 9 = 9$ - For $x=3$: $(-1)^3 3^3 = -1 \times 27 = -27$ - For $x=4$: $(-1)^4 3^4 = 1 \times 81 = 81$ - For $x=5$: $(-1)^5 3^5 = -1 \times 243 = -243$ 4. Now sum all these values: $$-3 + 9 - 27 + 81 - 243$$ 5. Perform the addition step-by-step: $$(-3 + 9) = 6$$ $$6 - 27 = -21$$ $$-21 + 81 = 60$$ $$60 - 243 = -183$$ 6. Therefore, the value of the sum is: $$\boxed{-183}$$