Sequence and series is one of the most important subjects in mathematics. Although many students tend to be confused between the two, these two can be easily differentiated. Sequence and series can be differentiated, in which the order of the sequence always matters in the sequence, but it is not the case for series.
Sequence and series are the two important topics that the item list deals with. It is used in pattern recognition, for example, identifying the pattern of prime numbers and solving puzzles, etc. Furthermore, the series plays an important role in the differential equations and in the analysis process. In this article, let’s discuss the key difference between sequence and series in detail. Before that, we will see the brief definition of the sequence and series.
Definition of sequence and series in mathematics Sequence And Series/ tabular form
Sequence – Sequence is defined as the list of numbers that are ordered in a specific pattern. Each succession of numbers in the sequence is considered a term. For example, 5, 10, 15, 20, 25,… is a sequence. The three dots at the end of the sequence represent that the pattern will continue further. Here, 5 is the first term, 10 is the second term, 15 is the third term, and so on. Each term in the sequence can have a common difference, and the pattern will continue with the common difference. In the example above, the common difference is 5. The sequence can be classified into different types, such as:
- Arithmetic sequence
- Geometric sequence
- harmonic sequence
- Fibonacci sequence
Series: The series is defined as the sum of the sequence where the order of the elements does not matter. It means that the series is defined as the list of numbers with the plus symbol in the middle. The series can be classified as a finite series and an infinite series that depends on the types of sequence if it is finite or infinite. Note that the finite series is a series where the list of numbers has an ending, while the infinite series is endless. For example, 1 + 3 + 5 + 7 + .. is a series. The different types of series are:
- Geometric series
- Harmonic series
- Power Series
- Alternating series
- Exponent series (P series)
What is the difference between sequence and series?
Next, we show you a comparative table, with examples, of the main differences of the mathematical concepts of sequence and series
|The sequence is related to the organization of terms in a particular order (that is, the related terms follow each other) and the series is the sum of the elements of a sequence.||Series can also be classified as finite and infinite series.|
|In sequence, the order of the elements is the most important||In series, the order of the elements does not matter|
|The elements of the sequence follow a specific pattern||The series is the sum of elements in the sequence.|
|Example: 1, 2, 4, 6, 8 ,. . . . It is said that n are in a sequence and 1 + 2 + 4 + 6 + 8 .. . . It is said that n is in a series.||A finite series can be represented as m1 + m2 + m3 + m4 + m5 + m6 +. . . . . + mn|
|General form . Endless sequence like p1, p2, p3, p4, p5, p6 ,. . . . , pn ,. . . . . , is known as an infinite sequence.[Pme]Northi = 1||If m1 + m2 + m3 + m4 + m5 + m6 +. . . . . . + mn = Sn, then Sn is called the sum of n elements of the series.|
|General form .[PNorth]∞n = 1||General form . SNorth=∑Northr = 1subwayr|
|The order of a sequence matters. Therefore, a sequence 5, 6, 7 is different from 7, 6, 5.||However, in the case of the series 5 + 6 + 7 it is the same as 7 + 6 + 5.|
Sequence and series faq Sequence And Series/ tabular form
What is meant by arithmetic sequence?
In mathematics, arithmetic sequence, also known as an arithmetic progression where the difference between the two consecutive terms in the sequence must be a constant.
Write the next three terms in the given sequence 1, 4, 7,…. Sequence And Series/ tabular form
The next three terms in the sequence are 10, 13, 16. In this sequence, the difference between 1 and 4 is 3, and 4 and 7 is 3. So, the common difference of this sequence is 3. Therefore, 7 + 3 = 10, 10 + 3 = 13, 13 + 3 = 16.
What are the different types of series in mathematics?
The different types of series in mathematics are arithmetic series, harmonic series and geometric series, P series, exponential series and so on.
Definition of the finite sequence. Sequence And Series/ tabular form
If the number of terms in the sequence is finite or of fixed length, then it is called a finite sequence.
String definition with an example
Series is defined as the sum / sum of terms in a sequence. For example, 2, 4, 6, 8 is a sequence, so the series is written as 2 + 4 + 6 + 8.