polynomial sequences

Polynomial sequences are sets of numbers generated by polynomial functions, which are mathematical expressions involving variables raised to whole number powers, combined using addition, subtraction, and multiplication. A simple example is the sequence formed by the function \( f(n) = n^2 \), where \( n \) is a whole number: 0, 1, 4, 9, 16, etc. These sequences can exhibit patterns and growth behaviors, making them useful in various fields like science, economics, and computer science, helping in modeling and solving problems where relationships can be described by polynomials.