1, the definition, classification and general formula of sequence.

Definition of (1) series:

① Sequence: A series of numbers arranged in a certain order.

② Items in the series: every number in the series.

(2) Classification of series:

The classification standard type meets the requirements.

The number of items is limited, and so is the number of items in the sequence.

The number of items in an infinite sequence is infinite.

The increasing order of the size relationship between projects is an+1>; An where n ∈ n

The decreasing sequence an+ 1.

Constant sequence an+ 1=an.

(3) General formula of series:

If the relationship between the nth term of the series {an} and the serial number n can be expressed by a formula, then this formula is called the general term formula of this series.

2. Recursive formula of sequence.

If the first term (or previous terms) of the series {an} is known, and the relationship between any term an and its previous term an- 1(n≥2) (or previous terms) can be expressed by a formula, this formula is called the recursive formula of the series.

3. Understanding of the concept of sequence.

(1) series is a series of numbers arranged in a certain "order". A sequence is not only related to the numbers that make it up, but also to the arrangement order of these numbers, which is different from the disorder of elements in a set. Therefore, if the numbers that make up two series are the same, but the arrangement order is different, they are two different series.

(2) The number in the series can be repeated, but the elements in the set cannot be repeated, which is also the difference between the series and the set number.

4. Functional characteristics of the sequence.

Sequence is a special function whose domain is positive integer set N_ (or its finite set {1, 2,3, ..., n}), and the general term formula of sequence is the corresponding resolution function, that is, f(n)=an(n∈N_).