Jagat Singh

Progressions and Series

IIT JEE Mathematics

Algebra

Progressions and Series

Basic Concepts of Sequences and Pattern

Table of Content

Sequence and series 

Difference between Sequence and Set

Representation of a Sequence

Sequence and Pattern

Arithmetic Progression

Geometric Progression

Harmonic Progression

Arithmetico gomertic series
sum of seres by various methods

IIT JEE 2020 and 2021 Main and Advanced exam preparation. Know about detailed syllabus, best books, exam pattern and dates. Cover previous year question papers and book solutions from great educators.

IIT JEE

JEE Main and Advanced Preparation

Hindi

(Hindi) Sequence and Series for IIT JEE

Series & Progressions

Algebra

Mathematics

IITJEE, NEET UG and Foundation

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Course overview

a sequence is a list of objects (or events) which have been ordered in a sequential fashion; such that each member either comes before, or after, every other member. More formally, a sequence is a function with a domain equal to the set of positive integers. A series is a sum of a sequence of terms.

Sequences and Series (in Hindi)

arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

Example

2,4,6,8,10….is an arithmetic sequence with the common difference 2.

If the first term of an arithmetic sequence is a1 and the common difference is d, then the nth term of the sequence is given by:

an=a1+(n−1)dan=a1+(n−1)d

An arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, a1 and last term, an, divide by 2 in order to get the mean of the two values and then multiply by the number of values, n:

Sn=n2(a1+an)Sn=n2(a1+an)

(AP) Arithmetic Progressions (in Hindi)

An arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, a1 and last term, an, divide by 2 in order to get the mean of the two values and then multiply by the number of values, n:

Sn=n2(a1+an)

Sum and General Terms of AP (in Hindi)

The following ways are generally used for the selection of terms in an arithmetic progression. If the sum of five terms in Arithmetic Progression be given, assume the numbers as a - 2d, a - d, a, a + d and a + 2d. Here common difference is 2d

Selection of Terms in AP (in Hindi)

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3.

(GP) Geometric Progression (in Hindi)

The average of a set of numerical values, as calculated by adding them together and dividing by the number of terms in the set.

Arithmetic mean or AM (in Hindi)

the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product

Geometric Mean (GM) (in Hindi)

a sequence of quantities whose reciprocals are in arithmetical progression

Harmonic Progression (HP) (in Hindi)

AM-GM-HM Inequality. The arithmetic mean-geometric mean (AM-GM) inequalityasserts that the the arithmetic mean is never smaller than the geometric mean: fAM≥fGM. ... It can be used as a starting point to prove the QM-AM-GM-HM inequality.

AM GM HM Inequality (in Hindi)

Sum of Arithmetic Geometric Sequence. In mathematics, an arithmetico–geometric sequence is the result of the term-by-term multiplication of a geometric progression with the corresponding terms of an arithmeticprogression. ... The task is find the sum of first n term of the AGP.

(AGP) Arithmetico Geometric Series (in Hindi)

Learn how to find sum of all terms of a sequence by using its general term.

Sum of the First Terms of a Series. The sum of the terms of a sequence is called a series . If a sequence is arithmetic or geometric there are formulas to find the sum of the first terms, denoted , without actually adding all of theterms.

Sum of terms by its general term (in Hindi)

In this lesson , you will learn how to find general term of a given series by difference method

Difference method for some finite algebraic series. (A) If the general term, ur , of the series is in "product" form, you can add one more factor to the end of the general term ur , so as to form a sequence vr and then apply thedifference method.

Method of difference to find general term (in Hindi)

Learn how to use techniques and tips and concepts learnt in this course to simplify questions asked in previous year in iit jee exams

Questions asked in previous years (in Hindi)

Method of Differences. Subtracting (2) from (1), we get, an = a1 + [(a2–a1) + (a3–a2)+…+(an–an–1)]. Since the terms within the brackets are either in an A.P. or a G.P., we can find the value of an, the nth term. We can now find the sum of the n terms of the sequence as S = Σnk=1 ak.

Method of difference to find SUM (in Hindi)

Expected questions and Learn how to use techniques and tips and concepts learnt in this course to simplify questions asked in previous year in iit jee exams

PYQs and Expected questions on vector (in Hindi)

Learn how to convert th term of a series as diffeence of two terms to evaluate sum of series

Method of Differences. Subtracting (2) from (1), we get, an = a1 + [(a2–a1) + (a3–a2)+…+(an–an–1)]. Since the terms within the brackets are either in an A.P. or a G.P., we can find the value of an, the nth term. We can now find the sum of the n terms of the sequence as S = Σnk=1 ak.

Sum by changing nth term (in Hindi)

Sequence and series, important questions and soled using techniques and concepts learnt in this coure for IITJEE MATHS

Important Questions at a glance (in Hindi)

Method of difference for general term explanation (in Hindi)

Rth Differences of terms of series (in Hindi)

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Lessons

20 lessons • 4h 33m