1. General term formula and summation formula of arithmetic progression and geometric progression: This is the basis of the series, and it is necessary to master the general term formula and summation formula of arithmetic progression and geometric progression, and be able to solve one or the sum of the first n terms of the series according to known conditions.
2. Recursive series: Recursive series means that each item is a linear combination of the previous items. It is necessary to master the general term formula and summation formula of recursive sequence, and be able to solve the sum of one term or the first n terms of sequence according to known conditions.
3. Fibonacci series: Fibonacci series is a classical recursive series, which needs to master the properties and applications of Fibonacci series and be able to solve the sum of one or the first n terms of Fibonacci series.
4. Harmonic series: Harmonic series is a series composed of the reciprocal of exponential series. It is necessary to master the nature and application of harmonic series and be able to solve one term or the sum of the first n terms of harmonic series.
5. Square series and cubic series: Square series and cubic series mean that each term is the square or cube of the previous term. It is necessary to master the properties and applications of square series and cubic series, and to be able to solve one term of square series and cubic series or the sum of the first n terms.
6. Application problems of arithmetic progression and geometric progression: arithmetic progression and geometric progression have many problems in practical application, and it is necessary to master how to turn practical problems into those of arithmetic progression and geometric progression and solve them.
7. Comprehensive application problems of series: Comprehensive application problems usually involve the comprehensive application of multiple knowledge points, and it is necessary to master the nature and application of different types of series and be able to use knowledge flexibly to solve problems.
The above are the key problems of sequence in senior high school mathematics, and mastering these problems is very important for solving the problem of sequence in mathematics.