# CBSE Class 11 Mathematics Sequence And Series Notes

Download CBSE Class 11 Mathematics Sequence And Series Notes in PDF format. All Revision notes for Class 11 Mathematics have been designed as per the latest syllabus and updated chapters given in your textbook for Mathematics in Class 11. Our teachers have designed these concept notes for the benefit of Class 11 students. You should use these chapter wise notes for revision on daily basis. These study notes can also be used for learning each chapter and its important and difficult topics or revision just before your exams to help you get better scores in upcoming examinations, You can also use Printable notes for Class 11 Mathematics for faster revision of difficult topics and get higher rank. After reading these notes also refer to MCQ questions for Class 11 Mathematics given on studiestoday

## Revision Notes for Class 11 Mathematics Chapter 9 Sequences and Series

Class 11 Mathematics students should refer to the following concepts and notes for Chapter 9 Sequences and Series in Class 11. These exam notes for Class 11 Mathematics will be very useful for upcoming class tests and examinations and help you to score good marks

### Chapter 9 Sequences and Series Notes Class 11 Mathematics

Class -XI

Chapter 9: Sequence and Series

Chapter Notes

Top Definitions

1. A Sequence is an ordered list of numbers according to some rule. A sequence is denoted by n> n³1 = a1,a2,a3, …….an

2. The various numbers occurring in a sequence are called its terms.

3. A sequence containing finite number of terms is called a finite sequence. A finite sequence has last term.

4. A sequence which is not a finite sequence, i.e. containing infinite number of terms is called an infinite sequence. There is no last term in an infinite sequence.

5. A sequence is said to be an arithmetic progression if every term differs from the preceding term by a constant number. For example, sequence a1, a2, a3, … an, … is called an arithmetic sequence or an AP if an+1 = an + d for all n Î N , where d is a constant called the common difference of AP.

6. A is the arithmetic mean of two numbers a and b if a,A,b forms an arithmetic progression.

7. A sequence is said to be a geometric progression or G.P., if the ratio of any tem to its preceding term is same throughout. Constant Ratio is common ratio denoted by r.

8. If three numbers are in GP, then the middle term is called the geometric mean of the other two.

Top Concepts

1. A sequence has a definite first member, second member, third member and so on.

2. The nth term n> is called the general term of the sequence.

3. Fibonacci sequence 1, 1, 2, 3, 5, 8,.. … is generated by the recurrence relation given by

a1 = a2 = 1

a3 = a1 + a2……

an = an-2 + an-1, n > 2

4. A sequence is a function with domain the set of natural numbers or any of its subsets of the type {1, 2, 3, … k}.

5. The sum of the series is the number obtained by adding the terms.

6. General form of AP is a, a + d, a + 2d, ...a+(n-1)d. a is called the first term of the AP and d is called the common difference of the AP. d can be any real number.

7. If d>0 then AP is increasing if d< 0then AP is decreasing and d=0 then AP is constant.

8. For AP a , (a + d) , (a + 2d) , ... , (l - 2d) , (l - d), l   with first term a and common difference d and last term l  general term is l-(n-1)d.

9. Properties of Arithmetic Progression
i. If a constant is added to each term of an A.P., the resulting sequence is also an A.P.

ii. If a constant is subtracted from each term of an A.P., the resulting sequence is also an A.P.
iii. If each term of an A.P. is multiplied by a constant, then the resulting sequence is also an A.P.
iv. If each term of an A.P. is divided by a non – zero constant then the resulting sequence is also an A.P.

10. The arithmetic mean A of any two numbers a and b is given by
a+b / 2

11. General Form of GP: a, ar, ar2, ar3, ..... where a is the first term and r is the constant ratio r can take any non zero real number.
12. A sequence in geometric progression will remain in geometric progression if each of its terms is multiplied by a non zero constant.
13. A sequence obtained by the multiplying two GPs term by term results in a GP with common ratio the product of the common ratio of the two GPs.
14. The geometric mean (G.M.) of any two positive numbers a and b is given by ab .
15. Let A and G be A.M. and G.M. of two given positive real numbers a and b, respectively, then A ≥ G
Where A = a+b/2 , and G = √ab

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### CBSE Class 11 Mathematics Chapter 9 Sequences and Series Notes

We hope you liked the above notes for topic Chapter 9 Sequences and Series which has been designed as per the latest syllabus for Class 11 Mathematics released by CBSE. Students of Class 11 should download and practice the above notes for Class 11 Mathematics regularly. All revision notes have been designed for Mathematics by referring to the most important topics which the students should learn to get better marks in examinations. Studiestoday is the best website for Class 11 students to download all latest study material.

### Notes for Mathematics CBSE Class 11 Chapter 9 Sequences and Series

Our team of expert teachers have referred to the NCERT book for Class 11 Mathematics to design the Mathematics Class 11 notes. If you read the concepts and revision notes for one chapter daily, students will get higher marks in Class 11 exams this year. Daily revision of Mathematics course notes and related study material will help you to have a better understanding of all concepts and also clear all your doubts. You can download all Revision notes for Class 11 Mathematics also from www.studiestoday.com absolutely free of cost in Pdf format. After reading the notes which have been developed as per the latest books also refer to the NCERT solutions for Class 11 Mathematics provided by our teachers

#### Chapter 9 Sequences and Series Notes for Mathematics CBSE Class 11

All revision class notes given above for Class 11 Mathematics have been developed as per the latest curriculum and books issued for the current academic year. The students of Class 11 can rest assured that the best teachers have designed the notes of Mathematics so that you are able to revise the entire syllabus if you download and read them carefully. We have also provided a lot of MCQ questions for Class 11 Mathematics in the notes so that you can learn the concepts and also solve questions relating to the topics. All study material for Class 11 Mathematics students have been given on studiestoday.

#### Chapter 9 Sequences and Series CBSE Class 11 Mathematics Notes

Regular notes reading helps to build a more comprehensive understanding of Chapter 9 Sequences and Series concepts. notes play a crucial role in understanding Chapter 9 Sequences and Series in CBSE Class 11. Students can download all the notes, worksheets, assignments, and practice papers of the same chapter in Class 11 Mathematics in Pdf format. You can print them or read them online on your computer or mobile.

#### Notes for CBSE Mathematics Class 11 Chapter 9 Sequences and Series

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