Matrix Representation of Bi-Periodic Jacobsthal Sequence

Abstract

In this paper, we bring into light the matrix representation of bi-periodic Jacobsthal sequence, which we shall call the bi-periodic Jacobsthal Matrix sequence.. We obtained the nth general term of this new matrix sequence. By studying the properties of this new matrix sequence, the well-known Cassini or Simpson's formula was obtained. We then proceeded to find its generating function as well as the Binet formula. Some new properties and two summation formulas for this new generalized matrix sequence are also given. Keywords: Bi-periodic Jacobsthal sequence; Generating function; Binet formula.