First, the meaning of sequence
A sequence is an ordered number whose domain is a positive integer. Every number in a series is called an item in this series. The number ranked first is called 1 item of this series (usually also called the first item), the number ranked second is called the second item of this series, and so on, and the number ranked n is called the n item of this series, usually represented by an.
Second, the classification of series
1, and a series with a limited number of items is a "finite series"; A series with infinite terms is an infinite series.
2. Positive term sequence: A positive term sequence is a sequence in which all terms in the sequence are positive.
Starting from the second item, the series whose item is greater than its previous item is called increasing series (1, 2, 3, 4, 5, 6, 7);
Starting from the second term, the sequence with each term less than its previous term is called decreasing sequence (8, 7, 6, 5, 4, 3, 2,1);
Starting from the second item, some items are larger than the previous item, and some items are smaller than the previous item, which is called swing series;
Periodic series: a series with periodic changes is called a periodic series (trigonometric function);
Constant series: A series of equal terms are called constants.
Introduce three commonly used sequences.
I. arithmetic progression
Generally speaking, if the difference between each term of a series and its previous term is equal to the same constant from the second term, the series is called arithmetic progression, and this constant is called arithmetic progression's tolerance. Tolerances are usually represented by the letter d, and the sum of the first n terms is represented by Sn.
Second, geometric series
Generally speaking, if a series starts from the second term and the ratio of each term to its previous term is equal to the same constant, this series is called geometric series. This constant is called the common ratio of geometric series and is usually represented by the letter Q.
Third, equal sum sequence
"Equal sum series": In a series, if the sum of each term and its subsequent term is the same constant, then this series is called equal sum series, and this constant is called the sum of this series.
For a sequence, if the sum of any continuous k(k≥2) terms is equal, it is called an equal sum sequence, and its property is that it must be a cyclic sequence.