At which differences does the following polynomial sequence reach a constant value? an=2n4−n3 (1 point) Responses 4th differences 4th differences 2nd differences 2nd differences 3rd differences 3rd differences 1st differences

Answer 1

To determine at which differences the polynomial sequence defined by \( a_n = 2n^4 - n^3 \) reaches a constant value, we need to analyze the polynomial's degree.

The polynomial \( a_n \) is a 4th degree polynomial (since the highest power of \( n \) is 4). In general, for a polynomial of degree \( k \), the \( k \)-th differences will be constant. Therefore, the 4th differences of this polynomial will be constant.

Thus, the correct response is:

4th differences