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Sequence A succession of numbers arranged in a definite order according to a given certain rule is called sequence. A sequence is either finite or infinite depending upon the number of terms in a sequence. Progression A sequence whose terms follow certain patterns are more often called progression.

Sequence: Sequence is a function whose domain is a subset of natural numbers. It represents the images of 1, 2, 3,… ,n, as f 1 , f 2 , f 3 , …. Infinite Series: A series having infinite number of terms is called infinite series.

Arithmetic Progression AP. A sequence in which the difference of two consecutive terms is constant, is called Arithmetic Progression AP. Common difference in such case will be 2A. A sequence in which the ratio of two consecutive terms is constant is called GP. The constant ratio is called common ratio r. If A, G and H are arithmetic, geometric and harmonic means of two positive numbers a and b, then. A sequence in which every term is a product of a term of AP and GP is known as rithmeticogeometric progression.

Otherwise, in the similar way, we find series of higher order of differences and the nth term of the series. The sum of the series is denoted by the number e. Please send your queries to ncerthelp gmail. Link of our facebook page is given in sidebar. Copyright ncerthelp. Real Sequence: A sequence whose range is a subset of R is called a real sequence.

Progression: A sequence whose terms follow certain rule is called a progression. Finite Series: A series having finite number of terms is called finite series. Properties of Arithmetic Progression i If a sequence is a n AP, then its nth term is a linear expression in n, i.

Exponential Series The sum of the series is denoted by the number e. If pth, qth and rth term of geometric progression are also in geometric progression. If a, b and c are in AP, then xa, xb and xc are in geometric progression. Follow Us On Facebook. Please Share this webpage on facebook, whatsapp, linkdin and twitter. Facebook Twitter whatsapp Linkdin. Business Studies. Political Science.

Sequence A succession of numbers arranged in a definite order according to a given certain rule is called sequence. A sequence is either finite or infinite depending upon the number of terms in a sequence. Progression A sequence whose terms follow certain patterns are more often called progression. Arithmetic Progression AP A sequence in which the difference of two consecutive terms is constant, is called Arithmetic progression AP. If a constant is added or subtracted from each term of an AR then the resulting sequence is an AP with same common difference.

Infinite Sequence. Arithmetic Sequence or Progression. General term of Arithmetic Progression. Arithmetic Mean. Geometric Mean. Geometric progression.

Sequence: Sequence is a function whose domain is a subset of natural numbers. It represents the images of 1, 2, 3,… ,n, as f 1 , f 2 , f 3 , …. Infinite Series: A series having infinite number of terms is called infinite series. Arithmetic Progression AP. A sequence in which the difference of two consecutive terms is constant, is called Arithmetic Progression AP. Common difference in such case will be 2A.

In JEE Main, JEE Advanced and other engineering entrances exams it is important for the candidate to remember all the important series and progressions. Thus, it is recommended that a serious candidate has a clear understanding of sequences and series. Arithmetic Progression AP is defined as a series in which a difference between any two consecutive terms is constant throughout the series. This constant difference is called the common difference. GP is defined as a series in which ration between any two consecutive terms is constant throughout the series.

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In fact, this chapter will deal almost exclusively with series. However, we also need to understand some of the basics of sequences in order to properly deal with series. We will therefore, spend a little time on sequences as well. To be honest, many students will never see series outside of their calculus class. However, series do play an important role in the field of ordinary differential equations and without series large portions of the field of partial differential equations would not be possible. Sequences — In this section we define just what we mean by sequence in a math class and give the basic notation we will use with them. We will focus on the basic terminology, limits of sequences and convergence of sequences in this section.

Page 1 of 8. Sequences and Series Lecture Notes. Introduction. Although much of the mathematics we've done in this course deals with algebra and graphing.

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The formulae list covers all formulae which provides the students a simple way to study of revise the chapter. A sequence is an ordered collection of objects in which repetitions are allowed. There is a pattern in this sequence, the difference between any two consecutive numbers is 10, and thus this sequence is Progression.

Все застыли в ужасе. На экране перед ними высветилось сообщение об ошибке: НЕДОПУСТИМЫЙ ВВОД. ТОЛЬКО В ЦИФРОВОЙ ФОРМЕ - Черт его дери! - взорвался Джабба. - Только цифровой.

Падре Херрера, главный носитель чаши, с любопытством посмотрел на одну из скамей в центре, где начался непонятный переполох, но вообще-то это его мало занимало. Иногда кому-то из стариков, которых посетил Святой Дух, становилось плохо. Только и делов - вывести человека на свежий воздух. Халохот отчаянно озирался, но Беккера нигде не было .

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