Ok lets tackle these one at a time.
Sequence: Is an Enumerated collection of objects in which repetitions are allowed. Kind of like a set, it contains members (elements or terms). The number of elements (can be a fixed number or infinite) is called the lenght of the sequence.
Series: A series is, roughtly speaking, a description of the operation of adding infinitley many quantites, one after the other, to a given statting quantity. The study of sereis is a major part of calculus and its generalization, mathematical analysis.
Arithmetic: Is a Branch in mathmatics that usually deals with non negetive real numbers. It sometimes incluedes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them.
Geometric: Geometry is the area of mathmatics that deals with points, lines, space, or most commonly shapes. The meaning of geometric is relating to geometry according to its methods.
I hope this helped! best of luck!
