The arithmetic sequence can be explained as a, a + d, a + 2d, a + 3d, …Įach term in a geometric progression is obtained by multiplying the common ratio of the successive term to the preceding term. In a math series and sequence, a is considered to be the first term, d is the common difference, and an is known to be the nth term. Remember, mastery over these formulas is not just about memorization but about applying them intelligently to solve a wide range of problems. Regular practice and application of these formulas in problem-solving scenarios will enhance both speed and accuracy, contributing to a strong performance in the examination. Understanding these formulas equips aspirants with the tools needed to tackle diverse number series problems in JEE Main. Various series involving alternate signs, squares, cubes, etc., should be approached with specific formulas depending on the pattern. Nth term of a GP: The nth term of a GP can be found using the following formula:Ī harmonic sequence is one in which each term of an arithmetic sequence is multiplied by the reciprocal of that term. The geometric progression can be of two types: Finite geometric progression and an infinite geometric series. A series formed by using a geometric sequence is known as the geometric series. Nth term of an AP: The nth term of an AP can be found using the following formula:Ī geometric sequence is a sequence where the successive terms have a common ratio, which is obtained by multiplying or dividing a definite number with the preceding number. The arithmetic series is a series constructed by applying an arithmetic sequence. An arithmetic sequence is, for example, 1, 4, 7, 10. Some of the common types of sequence examples areĪn arithmetic sequence is one in which each term is either the addition or subtraction of a common term known as the common difference. is a sequence, then the corresponding series is given by S n = a 1 +a 2 +a 3 +. For example, if a 1, a 2, a 3, a 4, ……. Series is a sum of elements that follow a pattern. denotes the position of the term.Ī sequence can be defined based on the number of terms, which is either a finite sequence or infinite sequence. denotes the term of a sequence, then 1, 2, 3, 4, …. The sequences and series formulas for different types are tabulated below: Arithmetic. Let’s discussed all the topics one-by-one in detail.Ī sequence is an arrangement of any objects or a set of numbers in a particular order(manner) followed by some rule. a, (a+d)r, (a+2d)r2, (a+3d)r3, a+ (n1)drn1 where, a is the first term of the sequence, d is the common difference and r is the common ratio. An arithmetico-geometric series is the sum of consecutive terms in an arithmetico-geometric sequence defined as:, where and are the th terms of arithmetic and geometric sequences, respectively. Sequence and series include various important topics from which questions come directly or indirectly in exams. Maths Sequence and Series Important Concepts For JEE Main Important Topics of Sequence and Series Chapter
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