1, the first term a, the sum formula of arithmetic sequence of tolerance d;

S = (n/2)(2a + (n- 1)d).

Where s represents the sum of arithmetic progression and n represents the number of terms.

2. Sum formula of arithmetic sequence with the first term a, the last term l and the number of terms n:

S = (n/2)(a + l).

Where s stands for the sum of arithmetic progression.

3. Sum formula of arithmetic sequence with first term a, tolerance d and number of terms n..

S = (n/2)(2a + (n- 1)d).

Where s stands for the sum of arithmetic progression.

Series introduction:

A sequence of numbers arranged in a certain order is called a sequence. Every number in a series is called an item in this series. The number ranked first is called the 1 term of this series (usually also called the first term), the number ranked second is called the second term of this series ... the number ranked n is called the nth term of this series.

Application of sequence:

1, math:

Sequence is a basic concept in mathematics, which is widely used in calculus, linear algebra, probability theory and other fields.

2. Statistics:

Sequence is also widely used in statistics, especially time series. Time series analysis can reveal the trend, seasonality and other laws of economic and social research.

3. Physics:

Sequence also has applications in physics. For example, in the interference experiment of light, the law of interference fringes of light can be expressed by series; In all kinds of motion problems in physics, it can also be analyzed and calculated through sequence.

4, computer science:

In computer science, sequences are also widely used, such as algorithm design, data structure, artificial intelligence and so on.

In a word, sequence is one of the very basic and important concepts in mathematics and science, which is widely used in analysis and calculation in various fields. The sequence can be finite or infinite. Common series types are arithmetic progression and geometric progression.