We see sequences in almost every other situation. What are the Different Types of Sequence?
#SERIES AND SEQUENCES MATH AND SCIENCE INITIATIVE SERIES#
A series is formed by using the elements of the sequence and adding them by the addition symbol. The sequence and the series of the same type, both are made up of the same elements (elements that follow a pattern). What is the Similarity Between Sequence and Series? The geometric progression can be of two types: Finite geometric progression and infinite geometric progression. A series formed by using geometric sequence is known as the geometric series for example 1 + 4 + 16 + 64. What is Geometric Sequence and Series?Ī geometric sequence is a sequence where the successive terms have a common ratio. A series can be written using sigma notation. A series formed by using an arithmetic sequence is known as the arithmetic series for example 1 + 4 + 7 + 10. ) What are Arithmetic Sequence and Series?Īn arithmetic sequence is a sequence where the successive terms are either the addition or subtraction of the common term known as common difference. Example of series: Fourier series: f(x) = 4h/π ( sin(x) + sin(3x)/3 + sin(5x)/5 +. 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. In sequence, elements are placed in a particular order following a particular set of rules, a definite pattern of the numbers is important, and the order of appearance of the numbers is important. What is the Difference Between Sequence and Series? Series is formed by adding the terms of a sequence. The sequence is the group or sequential arrangement of numbers in a particular order or set of rules. Sequence and series are used in mathematics as well as in our daily lives. The sum of the infinite GP formula is given as S n = a/(1−r) where |r|The formula for the nth term of a geometric progression whose first term is a and common ratio is r is a n = ar n−1.The summation of all the numbers of the sequence is called series. Using this formula, we can calculate any number of the Fibonacci sequence. Each successive term is obtained in a geometric progression by multiplying the common ratio to its preceding term. This is also called the Recursive Formula.In general, the arithmetic sequence can be represented as a, a+d, a+2d, a+3d.In an arithmetic sequence and series, a is represented as the first term, d is a common difference, a n as the nth term, and n as the number of terms.The following points are helpful to clearly understand the concepts of sequence and series.
Infinite series: S n = a/(1−r) for |r| 1 The various formulas used in geometric sequence are given below: Geometric sequenceįinite series: S n = a(1−r n)/(1−r) for r≠1, and S n = an for r = 1 Successive term – Preceding term or a n - a n-1 The various formulas used in arithmetic sequence are given below: Arithmetic sequence Formulas related to various sequences and series are explained below: Arithmetic Sequence and Series Formula These formulas are different for each kind of sequence and series. 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.
A series formed by using harmonic sequence is known as the harmonic series for example 1 + 1/4 + 1/7 + 1/10. Harmonic Sequence and SeriesĪ harmonic sequence is a sequence where the sequence is formed by taking the reciprocal of each term of an arithmetic sequence. The geometric progression can be of two types: Finite geometric progression and infinite geometric series. Geometric Sequence and SeriesĪ geometric sequence is a sequence where the successive terms have a common ratio. A knowledge of financial mathematics enables analysis and interpretation of different financial situations, the calculation of the best options for the circumstances, and the solving of financial problems. A series formed by using an arithmetic sequence is known as the arithmetic series for example 1 + 4 + 7 + 10. The topic Financial Mathematics involves sequences and series and their application to financial situations. The types of sequence and series are:Īn arithmetic sequence is a sequence where the successive terms are either the addition or subtraction of the common term known as common difference. There are various types of sequences and series, in this section, we will discuss some special and most commonly used sequences and series.
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