On the ratios and geometric boundaries of complex Horadam sequences

Abstract Horadam sequences are second-order linear recurrences in the complex plane which depend on two initial conditions and two recurrence coefficients which are complex numbers. Recently, numerous papers have been devoted to the periodicity of these sequences, as well as to generalizations and applications. In this paper we investigate aspects related to the sequence of rations of consecutive terms and geometric bounds of Horadam sequences. We also propose some directions for further study.