The polynomial sequence that shows that the terms of the 2nd differences are constant is a quadratic polynomial.
A quadratic polynomial can be represented in the form:
\[ f(n) = an^2 + bn + c \]
where \( a \), \( b \), and \( c \) are constants. When you calculate the first differences and then the second differences of the values generated by this polynomial, the second differences will be constant.
In contrast, linear polynomials have constant first differences, and cubic polynomials have constant third differences. Thus, it is specifically quadratic polynomials that yield constant second differences.