# Senior 2 # Introduction Senior 2 has two characteristics: First, the teaching progress is fast. You must complete two years of courses in one year. Second, the novelty of senior one has passed, and it is still far from the college entrance examination. It's the easiest time to go crazy and go far. Causes: psychological confusion period, slow academic progress period, loose self-discipline, easy to go astray, screening period of big waves and sand scouring. Therefore, facing the challenge of senior two, it is of great significance and urgency to recognize yourself and your tasks. No Senior Two Channel has compiled "arithmetic progression Knowledge Point Induction" for you, hoping to help you with your study!

one

1. arithmetic progression general term formula

an=a 1+(n- 1)d

When n= 1, a 1=S 1.

When n≥2, An=Sn-Sn- 1.

An=kn+b(k, b is constant) Deduction process: an=dn+a 1-d makes d=k, a 1-d=b, then an = KN+B is obtained.

2. Arithmetic average term

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.

This is very important: A=(a+b)÷2

3. The sum of the first n items

Derive the first n terms and formulas by inverse addition;

Sn=a 1+a2+a3+ +an

= a 1+(a 1+d)+(a 1+2d)++[a 1+(n- 1)d]①

sn = an+an- 1+an-2 ++ a 1

= an+(an-d)+(an-2d)++[an-(n- 1)d]②

get 2sn =(a 1+an)+(a 1+an)++(a 1+an)(n)= n(a 1+an)

∴Sn=n(a 1+an)÷2

The sum of the first n terms of arithmetic progression is equal to half of the product of the sum of the first two terms and the last two terms:

sn = n(a 1+an)÷2 = na 1+n(n- 1)d÷2

Sn=dn2÷2+n(a 1-d÷2)

There are also

a 1 = 2sn \n-an =[sn-n(n- 1)d \2]\n

an=2sn÷n-a 1

Interestingly, S2n- 1=(2n- 1)an, S2n+1= (2n+1) an+1.

4. Properties of arithmetic series

1. the relationship between any two am and an is:

an=am+(n-m)d

It can be regarded as arithmetic progression's generalized general term formula.

Secondly, from the definition and general formula of arithmetic progression, we can also derive the first n terms and formulas:

a 1+an = a2+an- 1 = a3+an-2 =…= AK+an-k+ 1，k∈N*

3. if m, n, p, q∈N* and m+n=p+q, then am+an=ap+aq.

Fourth, for any k∈N*, there is

Sk, S2k-Sk, S3k-S2k, …, Snk-S(n- 1)k… into arithmetic progression.

two

1 If the sum of the first n terms of arithmetic progression {an} is Sn and a2+a3=6, the value of S4 is ().

12b . 1 1c . 10d . 9

2 Establish arithmetic progression? Ann? The sum of the first n terms of is Sn, if a11,a4? A66, then when Sn takes the minimum value, n is equal to ().

A.6B.7C.8D.9

The sum of the first n terms of arithmetic progression is Sn. If S2? 4、S4？ 20, what about the tolerance d of this series? ()

I, 2B, 3C, 6D, 7

4 arithmetic progression {an}, a3? a4？ a5？ 84，a9？ 73.

Find the general formula and serial number of sequence {an}