On the General Linear Recursive Sequences

Linear Recursive Sequences

A sequence is an infinite list of numbers, like The numbers in the sequence are called its terms. The general form of a sequence is a 1 , a 2 , a 3 ,. .. where a n is the n-th term of the sequence. In the example (1) above, a 1 = 1, a 2 = 2, a 3 = 4, and so on. The notations {a n } or {a n } ∞ n=1 are abbreviations for a 1 , a Occasionally the indexing of the terms will start with something oth...

on the effect of linear & non-linear texts on students comprehension and recalling

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On the Appearance of Primes in Linear Recursive Sequences

We present an application of difference equations to number theory by considering the set of linear second-order recursive relations,Un+2( √ R,Q) =RUn+1 −QUn,U0 = 0,U1 = 1, and Vn+2( √ R,Q) =RVn+1 −QVn, V0 = 2,V1 = √ R, where R and Q are relatively prime integers and n∈ {0,1, . . .}. These equations describe the set of extended Lucas sequences, or rather, the Lehmer sequences. We add that the r...

General form of some rational recursive sequences

In this note, we study the general form of some rational recursive sequences. By some modification of the methods and ideas, as well as the transformation from the paper [K. The global attractivity of the rational difference equation y n = y n−k +yn−m 1+y n−k yn−m , Appl. Math. Lett. 20 (2007), 54–58], we give a new proof for the conjectures posed therein.

Intersections of Second - Order Linear Recursive Sequences