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The concept of sequence and series is one of the most fundamental concepts in Arithmetic. When it comes to numbers, sequences are the grouped arrangement of numbers that is done in an orderly manner according to some specified principles, whereas a series is the sum of the parts in the sequence. Examples of sequences with four elements are as follows: 2, 4, 6, 8, where 2 + 4 + 6+ 8 corresponds to a series with four elements, with a sum of the series or a value of the series equal to twenty.
There are many different sorts of sequences and series, each of which is distinguished by the set of rules that are used to construct the sequence or series. The terms sequence and series are defined in greater detail below.
What is the difference between Sequence and Series?
It is the grouping or sequential arrangement of numbers in a specific order or according to a set of criteria that is known as a sequence. A series is established by joining the terms of a sequence together. It is possible for a single phrase to appear in multiple locations within a sequence. An infinite sequence and a finite sequence are two different types of sequences. A series is defined by combining the terms of a sequence together. In some circumstances, it is also feasible to have a series with an infinite number of terms.
Let us use an example to better grasp this. When there is a common difference of 2 between any two words, the sequence 1, 3, 5, 7, 9, 11… is formed. Unless an upper limit is specified, the sequence will continue to increase indefinitely. Arithmetic sequences are a form of sequence that is used to represent numbers. After that, if we put the numbers in the sequence together, such as 1+3+5+7+9…, we will have a series of the numbers in the sequence. Arithmetic series are the types of series that fall within this category.
SEQUENCE | SERIES |
During the process of sequencing, items are placed in a specific order according to a specific set of rules. | It is unnecessary to arrange the elements in a sequential manner in a series. |
It is simply a collection (set) of items that are organised in a certain way. | It is made up of a collection of pieces that follow a pattern. |
The order in which the numerals occur is very crucial. | It makes no difference in whatever order the items appear. |
As an illustration, consider the following harmonic sequence: 1, 1/2, 1/3, 1/4,… | As an illustration, consider the harmonic series: 1 + 1/2 + 1/3 + 1/4 +… |
Conclusion
A sequence can be defined as an arrangement of numbers in a specific order that follows a set of rules. Make a list of the patterns you notice in your daily life and write them down. Graphs, geometry, mandalas, snail shells, flower petals, and so on are examples of what you can draw. All of these things can be calculated and expressed numerically in some way. This mathematical description of such patterns is investigated further under the headings of sequence and sequences. A sequence is any pattern that is set out in numbers and separated by commas and is termed as such.
By solving questions based on the formulas, it is possible to have a deeper understanding of the principles. Despite the fact that they are extremely similar to sets, the key difference is that in a sequence, individual terms might appear multiple times in different positions. When the number of terms in a series is equal to the length of the sequence, the sequence might be either limited or infinite in length. Detailed explanations of this idea can be found in class 11 mathematics. The ideas of sequence and series will be discussed in this section with the use of definitions, formulas, and illustrations.
