Generally speaking, if a series starts from the second term, the difference between each term and its previous term is equal to the same constant. This series is called arithmetic progression, and this constant is called arithmetic progression's tolerance zone. The tolerance is usually expressed by the letter D.

abbreviate

A.p. (arithmetic progression can be abbreviated as A.P.).

arithmetic mean

Arithmetic progression, which consists of three numbers A, A and B, can be called the simplest arithmetic progression. At this time, A is called the arithmetic average of A and B, which is very important: a = (a+b)/2.

General term formula

An = a1+(n-1) Dan = sn-s (n-1) (n ≥ 2) an = kn+b (k and b are constants).

Sum of the first n terms

sn = n(a 1+an)/2 = n * a 1+n(n- 1)d/2 sn=(d/2)*n^2+(a 1-d/2)n

nature

And the relationship between any two terms am and an is: an=am+(n-m)d, which can be regarded as arithmetic progression's generalized general term formula. From arithmetic progression's definition and general formula, we can also deduce the first n terms and formulas: A1+an = A2+an-1= A3+an-2 = … = AK+an-k+1,k ∈ {1. Then am+an = AP+aqsm-1= (2n-1) an, s2n+1 = (2n+1) an+1sk, S2k-Sk, S3k-S2k. Then a2 is the arithmetic average, then 2 times a2 equals a 1+a3, that is, 2a2=a 1+a3.

App application

In daily life, people often use arithmetic progression. For example, when grading the sizes of various products, when the maximum size is not much different from the minimum size, they often grade according to arithmetic progression. If it is arithmetic progression, and an = m and am = n, then a (m+n) = 0.

References:

/view/39749.htm

There is also geometric series.