In the related problems of finding the general term of series, we often encounter the problem of finding the general term that is neither arithmetic progression nor geometric progression, especially the problem that two adjacent terms of series are linear. In the old textbooks, we can induce and guess by incomplete induction, and then prove it by mathematical induction. However, in the new textbook, mathematical induction is deleted, so it should be avoided.

Construct the formula of geometric series or arithmetic series and find the general term. Construction method is in the process of solving some mathematical problems, through the full analysis of conditions and conclusions, sometimes it will be associated with appropriate auxiliary models, thus promoting the transformation of propositions and generating new problem-solving methods. The characteristic of this way of thinking is "construction". If the recursive formula of sequence is given under known conditions and the general formula of sequence is required, this kind of problem is usually difficult, but the application of construction method often gives people a refreshing feeling. For reference.

1. Construct arithmetic progression or geometric progression.

Because of the general formulas of arithmetic progression and geometric progression, it is obviously an effective method to construct arithmetic progression or geometric progression for some recursive sequence problems.