1, the general formula of arithmetic progression: an=a 1+(n? 1) D. This formula describes the relationship between the general term of arithmetic progression and the first term, tolerance and number of terms. Where an stands for the nth term, a 1 stands for the first term, and d stands for tolerance.
2. arithmetic progression's summation formula: Sn=2n(a 1+an). This formula is used to calculate the sum of the first n terms of arithmetic progression. Where Sn represents the sum of the first n terms, and a 1 and an represent the first term and the n term respectively.
3. General formula of geometric series: an=a 1qn? 1。 This formula describes the relationship between the general term of geometric series and the first term, common ratio and number of terms. Where an represents the nth term, a 1 represents the first term, and q represents the common ratio.
4. Sum formula of equal ratio series: Sn= 1? qa 1( 1？ Qn). This formula is used to calculate the sum of the first n terms of geometric series. Where Sn represents the sum of the first n terms, a 1 represents the first term, and q represents the common ratio.
5. The summation formula of the splitting term is ∑ i =1ni (i+1)1= n+1n. This formula is used to calculate the type of destructive summation of split terms, such as 2 1? 3 1+4 1? 5 1 and so on. By splitting each item, the offset result is obtained.
Application fields of sequences:
1. Financial field: Series has important applications in the financial field, such as calculating interest and return on investment. Using the general formula and summation formula of arithmetic progression and geometric progression, we can quickly calculate the answers to various financial questions.
2. Mathematical modeling: Series is a mathematical model, which can describe many natural phenomena and practical problems. For example, population growth, bacterial reproduction, population growth and other issues can be analyzed through a series of modeling.
3. Computer Science: Sequences are also widely used in computer science, such as sorting algorithm and hash algorithm. In addition, some data structures, such as linked lists and queues, can also be regarded as extensions of series.
4. Physics: There are many problems in physics that require the knowledge of series, such as quantum mechanics, statistical mechanics and other fields. When solving some physical problems, more accurate and concise solutions can be obtained by using the method of sequence.