Asian Journal of Mathematics & Statistics1994-54182077-2068Asian Network for Scientific Information10.3923/ajms.2018.18.26Ahmad TarrayTanveerAhmad NaikParvaizAhmad NajarRiyaz12018111Background and Objectives: Fibonacci sequence is a sequence of positive integers that has been studied over several years. The aim of this paper was to suggest new generalized Fibonacci sequence to a particular class of recursive sequence. Materials and Methods: The equilibrium point of the model was investigated and a new sequence. The matrix method was applied to perform the generalization. Results: The nth power of the generating matrix for this generalized Fibonacci sequence was established and some basic properties of this sequence were obtained by matrix methods. Conclusion: Cassini’s identity and Binet’s formula for the generalized Fibonacci sequence was obtained.]]>Bilgici, G.,2014Tasyurdu, Y., N. Cobanoglu and Z. Dilmen,2016Horadam, A.F.,1965Silvester, J.R.,1979Demirturk, B.,2010Uygun, S. and H. Eldogan,2016Godase, A.D. and M.B. Dhakne,2014Catarino, P. and P. Vasco,2013Catarino, P.,2013Borges, A., P. Catarino, A.P. Aires, P. Vasco and H. Campos,2014Wloch, I., U. Bednarz, D. Brod, A. Wloch and M. Wolowiec-Musial,2013Wani, A.A., V.H. Badshah, S. Halici and P. Catarino,2018Wani, A.A., G.P.S. Rathore, V.H. Badshah and K. Sisodiya,2018Rathore, G.P.S., A.A. Wani and K. Sisodiya,2016Wani, A.A., G.P.S. Rathore and K. Sisodiya,2017Naik, P.A. and K.R. Pardasani,2018Naik, P.A. and K.R. Pardasani, 2014+/K^{+} Pump and Na^{+}/Ca^{2+} exchanger on calcium distribution in oocytes in presence of buffers.]]>