What are second-order and multi-order arithmetic progressions? What is the formula for summing a second-order arithmetic progression?

Sequence is one of the important contents of high school mathematics. Arithmetic sequence is learned in the first year of high school. It belongs to the compulsory fifth course of the People's Education Edition, that is, in the second semester of high school and the first semester of high school. It not only has a wide range of practical applications, but also plays a role in connecting the past and the future. On the one hand, as a special function, sequence is inseparable from the function idea; on the other hand, learning sequence is also a preparation for further learning the limit of sequence and other contents. Arithmetic sequence is to further deepen and expand the knowledge of sequence on the basis of students learning the relevant concepts of sequence and giving two methods of sequence, general formula and recursive formula. The most basic is the second-level arithmetic sequence, followed by multi-level arithmetic sequence. Next, let's look at the summation formula of the second-level arithmetic sequence.

Contents of this article

1. In which grade do we learn arithmetic progression?

2. What is a second-order arithmetic sequence?

3. What is a multi-level arithmetic progression?

4. What is the formula for summing a second-order arithmetic sequence?

In which grade do we learn arithmetic progression?

Arithmetic sequence is learned in the first year of high school. It is a compulsory course in the People's Education Press version, which is learned in the second semester of the second year of high school and the first semester of the second year of high school.

An arithmetic sequence is a sequence in which the difference between each term and the previous term from the second term onwards is equal to the same constant, usually represented by A or P. This constant is called the common difference of the arithmetic sequence, and the common difference is usually represented by the letter d.

For example: 1, 3, 5, 7, 9...2n-1. The general formula is: an=a1 (n-1)*d. The first term a1=1, the common difference d=2. The formula for the first n terms is: Sn=a1*n [n*(n-1)*d]/2 or Sn=[n*(a1 an)]/2.

Note: All the above n are positive integers.

What is a second-order arithmetic sequence?

A set of numbers that are divided twice to obtain an arithmetic sequence is called a multi-level arithmetic sequence. If a set of numbers has a common difference, then this set of numbers is an arithmetic sequence; if two adjacent numbers are divided once to obtain an arithmetic sequence, then it is called a second-level arithmetic sequence; if two numbers are divided twice to obtain an arithmetic sequence, then it is called a third-level arithmetic sequence. Arithmetic sequences above the second level are called multi-level arithmetic sequences.

What is a multi-level arithmetic progression?

A set of numbers that are divided twice to obtain an arithmetic sequence is called a multi-level arithmetic sequence. If a set of numbers has a common difference, then this set of numbers is an arithmetic sequence; if two adjacent numbers are divided once to obtain an arithmetic sequence, then it is called a second-level arithmetic sequence; if two numbers are divided twice to obtain an arithmetic sequence, then it is called a third-level arithmetic sequence. Arithmetic sequences above the second level are called multi-level arithmetic sequences.

What is the formula for summing a second-order arithmetic sequence?

The formula for summing a second-order arithmetic sequence is a(n)=An^2 Bn C. An arithmetic sequence is a sequence in which the difference between each term and the previous term is equal to the same constant starting from the second term, usually represented by A or P. This constant is called the common difference of the arithmetic sequence, and the common difference is usually represented by the letter d.

Arithmetic sequence is a common type of sequence, which can be expressed as AP. If the difference between each term and the previous term of a sequence from the second term onwards is equal to the same constant, this sequence is called an arithmetic sequence, and this constant is called the common difference of the arithmetic sequence, which is usually represented by the letter d. For example: 1, 3, 5, 7, 9... (2n-1). The general formula of the arithmetic sequence {an} is: an=a1 (n-1)d. The formula for the sum of the first n terms is: Sn=n*a1 n(n-1)d/2 or Sn=n(a1 an)/2.