Derivation of the Quadratic Arithmetic Sequence and its Applications Using the Arithmetic Sequence in the Kuwait National Curriculum for Grade 10

Arithmetic sequences are fundamental and important mathematical concepts included in the Grade 10 curriculum in the State of Kuwait. A new formula for the quadratic arithmetic sequence has been derived based on the fundamental principles of arithmetic sequences. This quadratic sequence is characterized by having constant second differences between its terms. A quadratic arithmetic sequence is defined as a numerical sequence where the difference between consecutive terms is not constant, but the difference between these differences (i.e., the second differences) remains constant, making it a mathematical model that represents quadratic patterns.The results and conclusions were analyzed and verified using MATLAB, which enabled precise and efficient computations, as well as effective visual data representation.