To determine at which differences the polynomial sequence \( a_n = 2n^4 - n^3 \) reaches a constant value, we start by identifying the degree of the polynomial.
The polynomial \( a_n \) is a quartic polynomial (degree 4) since the highest power of \( n \) is 4.
In general:
- For a polynomial of degree \( k \), the \( k \)-th differences will result in a constant value.
- The \( (k-1) \)-th differences will be a polynomial of degree 1, and so on.
Since \( a_n \) is a polynomial of degree 4, we need to look at the 4th differences to find a constant value.
Thus, the correct response is:
4th differences