Asymptotic Behavior of Limiting Ratios of Generalized Recurrence Relations

Abstract

The most famous Fibonacci sequence possess a rather easy recurrence relation in which except the first two terms, each term is the sum of two previous terms. In this paper, I try to generalize the recurrence relation of Fibonacci sequence with respect to number of terms as well as considering not just the consecutive terms but terms whose index are in Arithmetic Progression. With this consideration, I try to obtain the limiting ratio of the new sequence produced through such generalization. The answers obtained cover more general class of Fibonacci type sequences and will provide new insights in the discussion of such generalizations.