The sum of the first \( n \) consecutive numbers is given by the formula:
\[ S(n) = \frac{n(n+1)}{2} \]
This can be expressed as a polynomial function of degree 2 (specifically, a quadratic polynomial). To find which level of differences is constant, we need to consider the properties of polynomials:
- For a polynomial of degree \( k \), the \( k \)-th differences are constant.
- The first differences of a quadratic polynomial will be linear (degree 1), hence the second differences will be constant.
Since the given expression is a quadratic polynomial (degree 2), the second differences will be constant.
The correct response is therefore:
2nd differences