Question 4

The sum of 2025 consecutive odd integers is $$2025^{2025}$$. The largest of these odd numbers is

Solution

For an odd number of consecutive odd integers the sum equals the count times the middle term, so the middle term is $$\frac{2025^{2025}}{2025} = 2025^{2024}$$. There are 1012 terms above the middle one and consecutive odd numbers differ by 2. Hence the largest term is $$2025^{2024} + 2 \times 1012 = 2025^{2024} + 2024$$.