Difference Between Sequence And Series, Definition, Types, Important Topics For JEE 2024
Difference Between Sequence and Series : Read everything you need to know about the important concepts of numbers. Learn the difference between sequence and series.
Shrivastav 18 Jan, 2024
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Difference Between Sequence And Series : The mathematical concepts that deal with ordered sets of numbers are sequences and series. Despite their seeming similarities, there is a difference between sequence and series. Anyone studying mathematics or looking at mathematical patterns has to understand the difference between sequence and series. The difference between sequence and series in mathematics and statistics is sometimes unclear, leading to the misunderstanding that they are similar concepts. However, the concept of the sequence is different from that of the series in that the series refers to an arrangement in the specific order that related concepts follow one another; that is, it contains a first unit, a second unit, a third unit, and so on. We will discuss the difference between sequence and series in detail. Achieve JEE excellence with PW JEE Online Course . Join now to fulfill your engineering dreams. Before we discuss the difference between sequence and series, let’s first discuss the meanings of them.
Sequence Meaning
In the field of mathematics, an ordered collection of items or numbers, such as a1, a2, a3, a4, a5, a6,... are considered to be in a sequence if they satisfy a certain rule and have a defined value. The terms or components that make up the sequence are those that have a natural number as their value. Each word in a series has a relationship with the term that comes before and after it. Sequences often have a hidden rule or pattern which helps in determining the value of the next word. The function of number n (positive), which is thought of as the sequence's general term, is the nth term. A finite sequence is one that ends at the end of the series of integers a1, a2, a3, a4, a5, a6, and so on. It is denoted by the following: {a i } n i=1 An infinite sequence is one that never ends. For example, a1, a2, a3, a4, a5, a6, and so on are all represented by the following: {a n } ∞ n=1Types of Sequence
The sequence may be divided into many categories, including:- Arithmetic Sequence
- Geometric Sequence
- harmonic Sequence
- Fibonacci Sequence
Series Meaning
A series is created when terms from one sequence (an) are added. Similar to sequences, series may either be finite or infinite. A finite series, denoted by the notation a1 + a2 + a3 + a4 + a5 + a6 +...an, has a limited number of elements. As opposed to infinite series, which are expressed as a1 + a2 + a3 + a4 + a5 + a6 +... + an, where the number of terms is either infinite or non-finite. Sn is the sum of the n items in the sequence if a1 + a2 + a3 + a4 + a5 + a6 +... a = Sn. The Greek symbol sigma Ʃ is often used to denote the sum of terms.Types of Series
The various series types are as follows:- Geometric series
- Harmonic series
- Power series
- Alternating series
- Exponent series (P-series)
Difference Between Sequence and Series
Difference Between Sequence and Series : The following table lists some of the points of difference between sequence and series:| Difference Between Sequence and Series | ||
| Particulars | Sequence | Series |
| Definition | Organization of terms in a specific order | Summation of the elements of a sequence |
| Classification | Can be finite or infinite | Can be finite or infinite |
| Order of Elements | Order is crucial | Order does not matter |
| Pattern | Follows a specific pattern | Represents the sum of sequence elements |
| Example | Sequence: 1, 2, 4, 6, 8, ... n | Series: 1 + 2 + 4 + 6 + 8 ... n |
| Representation | Finite series: m1 + m2 + m3 + ... + mn | Infinite sequence: p1, p2, p3, ... pn |
| Order Importance | Order matters (e.g., 5, 6, 7 is different from 7, 6, 5) | Order does not matter (e.g., 5 + 6 + 7 is the same as 7 + 6 + 5) |
Some Important Points of Sequence and Series
To understand sequence and series concepts properly, read the following points.- A is the first term, d is the common difference, an is the nth term, and n is the total number of terms in an arithmetic sequence or series.
- The arithmetic sequence may be written as a, a+d, a+2d, a+3d,... in general.
- In a geometric progression, each subsequent term is generated by multiplying the common ratio by the previous term.
- The equation a = arn−1 represents the nth term of a geometric progression with an as the first term and r as the common ratio.
- Sn = a/(1−r) is the formula for the infinite GP sum, when |r|<1.
Difference Between Sequence and Series FAQs
Q.1. What is the basic difference between sequence and series?
Ans. An arrangement of numbers in a certain order is called a sequence. A series, on the other hand, is characterized as the total of a sequence's elements.
Q.2: What does the term "arithmetic sequence" mean?
Ans. The difference between the two terms that follow one another in an arithmetic sequence, is commonly referred to as an arithmetic progression.
Q.3: What is a sequence example?
Ans. Numbers (referred to as "terms") in an ordered list are termed sequences, and examples of such lists are 2, 5, 8.
Q.4: What is the 2 4 8 16 sequence called?
Ans. An example of a geometric sequence, also known as a geometric progression (GP), is the sequence of numbers 1, 2, 4, 8, 16...
Q.5: What is the sequence formula?
Ans. An arithmetic sequence's nth term may be found using the formula an=a1+(n-1)d. Any term in an arithmetic sequence may have its value determined through this formula.
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