The essay discusses the characters of the second order linear recurrent sequence, which any number three , number four and number five terms of sequence nestie up, and develops the definition of the arithmetical progress and the geometric series in the united form according to these characters.

By using both of mathematical induction and method of undetermined coefficient,it is proved that some univariate equations of higher degree with integral coefficient have unique positive real solution,then the general terms of two nonlinear recurrent sequences are established,which generalize the results in Item 5,Paper One of 1989 National High School Mathematics Competition.