Sequence is any group of numbers with some pattern. Sequences and series are like sets, and the difference between them is that in a sequence, terms can occur multiple times in different positions. A series is the expansion of the multitude of terms of a sequence. All exercise questions, examples, miscellaneous are done step by step with detailed explanation for your understanding. Sequence and Series is the arrangement of numbers in a particular order and sum of the elements in the sequence. Solutions of Chapter 8 Sequences and Series of Class 11 NCERT book available free. It is not possible to have a finite number of elements in an infinite series, for example, a 1 + a 2 + a 3 + a 4 + a 5 + a 6 +…….a n +….Updated for new NCERT - 2023-2024 Edition. Series: The term a 1 + a 2 + a 3 + a 4 + a 5 + a 6 +……a n represents a finite number of terms in a finite series, which is expressed as a 1, a 2, a 3, a 4, a 5, a 6 ……a n. An infinite sequence, on the other hand, is never-ending, as in a 1, a 2, a 3, a 4, a 5, a 6 ……a n …. Sequence: For example, consider the following: A finite sequence is a list of numbers that terminates at the conclusion of the list: 1, 2, 3, 4, 5, 6…10. It makes no difference in whatever order the items appear.Īs an illustration, consider the following harmonic sequence: 1, 1/2, 1/3, 1/4,…Īs an illustration, consider the harmonic series: 1 + 1/2 + 1/3 + 1/4 +… The order in which the numerals occur is very crucial. It is made up of a collection of pieces that follow a pattern. It is simply a collection (set) of items that are organised in a certain way. It is not necessary to arrange the elements in a sequential manner in a series. The sorts of series that come within this category are arithmetic series.ĭuring the process of sequencing, items are placed in a specific order according to a specific set of rules. After that, we can combine the numbers in the sequence, such as 1+3+5+7+9…, to form a series of the numbers in the sequence. Arithmetic sequences are a type of sequence that represents numbers. The sequence will continue to expand indefinitely unless an upper limit is given. The sequence 1, 3, 5, 7, 9, 11,… is generated when any two words have a common difference of two. To further understand this, consider the following scenario. It is also possible to have a series with an infinite number of terms under particular circumstances. By merging the terms of a sequence, a series is formed. A finite sequence is different from an endless sequence. A single phrase can appear in many places within a sequence. The terms of a sequence are joined together to form a series. What is the difference between sequence and series?Ī sequence is defined as the grouping or sequential arrangement of numbers in a specified order or according to a set of criteria. The series can be classified as finite or infinite depending on the types of sequence made of, whether it is finite or infinite.įor example, 1+3+5+7+… is a series. Series is defined as the sum of all the elements in a sequence or it is defined as the sum of the sequence where the order of the terms does not matter. Fibonacci Number Sequenceįibonacci numbers form a sequence of numbers in which each of the terms is obtained by adding two preceding terms. Harmonic SequencesĪ harmonic sequence is a sequence where the reciprocals of all the terms of the sequence form an arithmetic sequence. Where, a is the first term m is the common ratio between the terms. General form- a, am, am2, am3, am4,…, amn The common ratio of a GP is obtained by taking the ratio between any one term in the sequence and dividing it by the previous term. Geometric SequenceĪ sequence in which each of the terms in a series is obtained by either multiplying or dividing a constant number with the former one is said to be a geometric sequence. Here, we observe that the common difference is 3. x1+ (n-1)m and so on, where m is the common difference. It is a sequence in which every term is found by adding or subtracting a definite number(common difference) from the preceding number. Below, the concepts sequence and series are described in further depth. All exercise questions, examples, miscellaneous are done step by step with detailed explanation for your understanding. There are many different types of sequences and series, each of which is distinguished by the set of rules employed to construct it. Updated for new NCERT - 2023-2024 Edition. The following are some examples of four-element sequences: 2, 4, 6, 8, where 2 + 4 + 6+ 8 is a four-element series with a sum of the series or a value of the series equal to twenty. Sequences are grouped arrangements of numbers that are done in an orderly manner according to some specified criteria, whereas a series is the sum of the components in a sequence. One of the most essential notions in Arithmetic is the concept of sequence and series.
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