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数列试题在高考试卷中一直占有重要位置,以递推形式给出的数列试题又是其中的重中之重,早就有人总结出这类试题中的递推规律常以α_(n+1)＝pα_n+q形式给出,并详细研究了这类试题的求解方法。但近几年来,随着分省命题的逐步推进,试题的数量、形式出现了空前的繁荣。同时,许多创新试题也脱颖而出,其中数列试题在递推形式的呈现上也有许多新的突破,某些试题的递推形式已由α_(n+1)＝pα_n+q演变为“g(α_(n+1))＝p·g(α_n)+q”的形式(其中g(x)在具体问题中是已知函数)。很显然,前者可看成后者当g(α_(n+1))=α_(n+1)的特例。
The series of test questions has always occupied an important position in the high test papers, and the series of test questions given in recursive form is one of the most important ones. It has long been concluded that the recurrence laws in this kind of questions often use α_(n+1). The form of =pα_n+q is given, and the method for solving such questions is studied in detail. However, in recent years, with the gradual advancement of the propositions of the provinces, unprecedented numbers and forms of questions have appeared in unprecedented prosperity. At the same time, many innovative test questions also come to the fore and many new breakthroughs have also been made in the presentation of recurrence forms for test questions. The recursive form of some test questions has evolved from α_(n+1)=pα_n+q to “g(α_(). n+1))=p·g(α_n)+q” (where g(x) is a known function in a particular problem). Obviously, the former can be seen as the special case of the latter when g(α_(n+1))=α_(n+1).