A.M. KIFILIDEEN Era of Generalization of Kifilideen Matrix Progression Sequence for Finite Terms with Decreasing Members for the Groups and (h+1) Members in the First Group

Kifilideen matrix had been in existence which emanate from the Kifilideen trinomial theorem for the arrangement of power combination of each term of the Kifilideen trinomial expansion in sequential order. The continuous interaction with the pattern, progression and sequential order in which the power combination of the positive and negative power of and of Kifilideen trinomial theorem are arranged in the Kifilideen matrix give incite that a general sequence can be developed to follow this pattern. This study presents the era of generalization of Kifilideen matrix progression sequence for finite terms with decreasing members for the groups and (h+1) members in the first group. Migration column/group and row/period values were used to form the bases of mathematical proof of the Kifilideen formulas of the Kifilideen general matrix progression sequence for the finite term invented. A general Kifilideen term and Kifilideen row column and Kifilideen term row column formulas were invented for the Kifilideen matrix progression sequence for the finite terms. This study proved that era of generalization of Kifilideen matrix progression sequence can be achieved in which Kifilideen general component formulas can be attained from the Kifilideen matrix progression sequence which had been proving valid and true using proof by mathematical induction. The terms of the sequence, group, row and column of the term of the sequence in the Kifilideen matrix and the value of any term can be obtained using the Kifilideen formulas invented for the Kifilideen generalize matrix progression sequence for the finite term.