1. **Problem Statement:** We want to determine which XP formula is more effective for reaching level 40. The formulas calculate total XP needed based on base XP per level $X$ and additional XP per level $Y$. 2. **Formulas:** Total XP to reach level $n$ is given by the sum of XP required for each level from 1 to $n$. The XP required for level $k$ is $X + (k-1)Y$. So total XP to reach level $n$ is: $$\text{Total XP} = \sum_{k=1}^n \left(X + (k-1)Y\right)$$ 3. **Simplify the sum:** $$\sum_{k=1}^n \left(X + (k-1)Y\right) = \sum_{k=1}^n X + \sum_{k=1}^n (k-1)Y = nX + Y \sum_{k=1}^n (k-1)$$ Since $\sum_{k=1}^n (k-1) = \frac{(n-1)n}{2}$, we get: $$\text{Total XP} = nX + Y \frac{(n-1)n}{2}$$ 4. **Calculate for each case with $n=40$:** - Case 1: $X=75$, $Y=25$ $$\text{Total XP}_1 = 40 \times 75 + 25 \times \frac{39 \times 40}{2} = 3000 + 25 \times 780 = 3000 + 19500 = 22500$$ - Case 2: $X=225$, $Y=15$ $$\text{Total XP}_2 = 40 \times 225 + 15 \times \frac{39 \times 40}{2} = 9000 + 15 \times 780 = 9000 + 11700 = 20700$$ 5. **Interpretation:** The second case requires less total XP (20700) to reach level 40 compared to the first case (22500). Therefore, the second combination ($X=225$, $Y=15$) is more effective in the long run for reaching level 40. **Final answer:** The second set of combinations is more effective because it requires less total XP to reach level 40.