![]() This works for any pair of consecutive numbers. įor sequence A, if we add 3 to the first number we will get the second number. The following sequences are arithmetic sequences: Sequence A: 5, 8, 11, 14, 17. ![]() X1, x2, x3,…, xn are the individual values up to nth terms.Sequences of numbers that follow a pattern of adding a fixed number from one term to the next are called arithmetic sequences. The harmonic mean is the reciprocal of the arithmetic mean, the formula to determine the harmonic mean “H” is ![]() If n and m are the two numbers then the geometric mean will be The average of two numbers is called Geometric Mean. In that case, the number A is the arithmetic mean of the numbers a and b. If we have two numbers a and b and include number A in between these numbers so that the three numbers will form an arithmetic sequence like a, A, b. The arithmetic mean is the average of two numbers. The formula of the Fibonacci Sequence is an = an-2 + an-1, n > 2 Arithmetic Mean The type of sequence that adds the value of the two terms before the ordered term, and obtains the next term is called the Fibonacci sequence. then nth term of the Harmonic Series is formulated as an = 1/a + (n-1)d Fibonacci Sequence Here, the common difference is denoted as d and there is (n - 1) number of d's in the nth term of the series. The reciprocal of the arithmetic series is called harmonic series. The formula of Sum of Geometric Series is Sn = a(1−rn)1−r Harmonic Sequence and Series Formulas The Formula of Geometric Series and Sequence of G.P where the nth term an of the geometric progression a, ar, ar2, ar3,…, is an=arn–1 if the ratio between every term to its preceding term is always constant then it is reportedly a geometric series. The sum of all the terms of the geometric sequences i.e. Sum of an Arithmetic Series formulas is Sn = n/2 2a+(n−1)d Geometric Sequences and SeriesĪ sequence in which every successive term has a constant ratio between them then it is called Geometric Sequence. Where a is the first term and d is the difference between the terms which is known as the common difference of the given series. Therefore, for i > 1Īi = ai-1 + d = ai-2 + d=. In an arithmetic sequence, if the first term is a1 and the common difference is d, then the nth term of the sequence is given by an= a1+ (n−1) dĪn arithmetic series is the sum of a sequence ai, i = 1, 2.n which each term is computed from the previous one by adding or subtracting a constant d. There are various types of sequences and series in this concept and they are explained here briefly:Īny sequence in which the difference between every successive term is constant then it is called Arithmetic Sequences. To get a good more grip on the sequence and series formulas we have discussed this list of formulas in a detailed way below along with types of sequences and series. The above list is very helpful for quick reference. If Sn denotes the sum up to n terms of G.P is Sn=a(1–rn)/1–r r≠1, Sn=a–rl/1–r l=arn where |r|G>H where A, G, H are usual notations.The geometric mean between a and b is G.M=±√ab. ![]() The nth term an of the geometric progression a, ar, ar2, ar3,… is an=arn–1.The sum of n A.M’s between a and b is =n(a+b)/2.a, a+d, a+2d,… then Sn=n/2(a+l) where l stands for the last term, Sn=n/2 If Sn denotes the sum up to n terms of A.P.The arithmetic mean between a and b is given by A.M=a+b/2.The nth term an of the Arithmetic Progression (A.P) a, a+d, a+2d,… is given by an=a+(n–1)d.Learn all the formulas of sequence and series on the daily basis and memorize them while solving any of the sequence and series related problems in homework, assignments, or main examinations. Also, you will find the formulas for a common difference between two subsequent terms in an arithmetic sequence and a common ratio between consecutive terms in a geometric sequence or series. The following list of sequences and series formulas helps kids to find the nth term, the sum of the n terms of the arithmetic sequence and series, geometric sequence and series, and harmonic sequence and series. For example, the series is 10+20+30+40+.+n, where n is the nth term. Series: The sum of sequences is the definition of a series. where 1,2,3 are the position of the numbers and n is the nth term. The common representation of the sequence is x1,x2,x3.xn. Sequence: An arrangement of numbers in a certain order as per the rules is defined as a sequence.
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