(untitled) (Research, Society and Development, 2024)
The objective of this article is to present a study on First and Second Order Geometric Progressions. A new approach will be presented for determining the general terms of the 1st and 2nd order Geometric Progression. In this new method, it is assumed that a generating function formed by products of exponential functions, where their bases are constants to be determined, is the general term of Geometric Progression. To determine the constants of the bases of the functions, the quotient operator in Geometric Progression (an) is used, generating new sequences ( . The first terms of (an), ( . are compared to the corresponding elements of the generating function producing a 3x3 nonlinear system, for P.G. second order and a 2x2 system if it is first order PG The solutions of these systems determine the bases of the respective generating functions and consequently establish the formulas of the general terms of PG second and first order. Among the results, some problems involving first and second-order geometric progressions will be presented as applications of the progressions.