What is the difference between sequences and series

The types of sequence and series are:. An arithmetic sequence is a sequence where the successive terms are either the addition or subtraction of the common term known as common difference. For example, 1, 4, 7, 10, A geometric sequence is a sequence where the successive terms have a common ratio. For example, 1, 4, 16, 64, The geometric progression can be of two types: Finite geometric progression and infinite geometric series. A harmonic sequence is a sequence where the sequence is formed by taking the reciprocal of each term of an arithmetic sequence.

There are various formulas related to various sequences and series by using them we can find a set of unknown values like the first term, nth term, common parameters, etc. These formulas are different for each kind of sequence and series.

Formulas related to various sequences and series are explained below:. In sequence, elements are placed in a particular order following a particular set of rules, a definite pattern of the numbers is important, and order of appearance of the numbers is important. In series, the order of the elements is not necessary, the pattern of the numbers is not important, and the order of appearance is not important. The geometric progression can be of two types: Finite geometric progression and infinite geometric progression.

The sequence and the series of the same type, both are made up of the same elements. A series is formed by using the elements of the sequence and joining them by the addition symbol. In mathematics, an ordered set of objects or numbers, like a 1 , a 2 , a 3 , a 4 , a 5 , a 6 ……a n…. The members of the sequence are called term or element which is equal to any value of the natural number.

Every term in a sequence is related to the preceding and succeeding term. In general, sequences have a hidden rules or pattern, which helps you find out the value of the next term. The nth term is the function of integer n positive , regarded as the general term of the sequence. A sequence can be finite or infinite.

The addition of the terms of a sequence a n , is known as series. Arithmetic Progression A. Arithmetic Progression is a sequence in which there is a common difference between the consecutive terms such as 2, 4, 6, 8 and so on.

It is also abbreviated as A. Thus we can define Arithmetic Sequence as. A sequence x 1,, x 2 ,x 3 , Is called an Arithmetic Progression, if there exists a constant number m such that,.

The constant m is called the common difference of the A. Thus we can write it as,. Where x is the first term. Geometric Sequence. A sequence in which each term is obtained by either multiplying or dividing a certain constant number with the preceding one is said to be a geometric sequence. For example:. Here we can see that there is a common factor 2 between each term.

The geometric sequence can be commonly written as,. Where a is the first term. Difference Between Sequence and Series.