## Abstract

In this paper, we give quadratic approximation of generalized Tribonacci sequence {*V _{n}*}

_{n}_{≥0}defined by

*V*=

_{n}*rV*+

_{n−1}*sV*+

_{n−2}*tV*(

_{n−3}*n*≥ 3) and use this result to give the matrix form of the

*n*-th power of a companion matrix of {

*V*}

_{n}

_{n}_{≥0}. Then we re-prove the cubic identity or Cassini-type formula for {

*Vn*}

_{n}_{≥0}and the Binet’s formula of the generalized Tribonacci quaternions.