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# Sequences and Series NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.1 9.2 9.3 9.4 Miscellaneous Free pdf Notes Study Material download-Anand Classes

NCERT solutions for class 11 maths chapter 9 Sequences and Series explain the importance of ‘sequences’ which play a significant role in a variety of human activities. We come across many examples of sequences in our everyday life, like the human population, money deposited in the banks, the value of any commodity over a number of years, etc. When any collection is ordered in such a way that its members are identified as first, second, third, and so on, then that collection is said to be listed in the form of a ‘sequence’. These NCERT solutions class 11 maths chapter 9 also talk about ‘progressions’, which are a type of sequence that follows a set of rules.

# Number of questions in each exercise of NCERT Solutions Class 11 Maths Chapter 9 – Sequences and Series

Till now, the students must be familiar with arithmetic progression; here, they will further explore arithmetic and geometric mean and the relationship between them. Also, they will learn how to calculate the sum of some special series involving consecutive natural numbers, squares, and cubes. The class 11 maths NCERT solutions chapter 9 in the pdf format can be accessed below and also download the exercise-wise solutions provided in the links below.

• NCERT Solutions Class 11 Maths Chapter 9 Ex 9.1
• NCERT Solutions Class 11 Maths Chapter 9 Ex 9.2
• NCERT Solutions Class 11 Maths Chapter 9 Ex 9.3
• NCERT Solutions Class 11 Maths Chapter 9 Ex 9.4
• NCERT Solutions Class 11 Maths Chapter 9 Miscellaneous Exercise

Understanding the number system, as well as the patterns it generates, is necessary for making sense of the world around us and solving day-to-day problems. The NCERT solutions have attempted to achieve the goal of teaching the sequences through real-life situations and exercises based on them. The pdf links below, provide access to the exercise questions in each part of the chapter of the NCERT solutions class 11

Mathematics is primarily concerned with the study of patterns in the environment and the understanding as well as manipulation of these patterns in order to solve real-world problems. As a result, it’s critical to comprehend how number sequences behave. The concept of sequences has several applications in various fields. Additionally, sequences also make their way into many other sister topics such as mathematical induction. An exercise-wise detailed analysis of NCERT Solutions Class 11 Maths Chapter 9 Sequences and Series is given below :

• Class 11 Maths Chapter 9 Ex 9.1 – 14 Questions
• Class 11 Maths Chapter 9 Ex 9.2 – 18 Questions
• Class 11 Maths Chapter 9 Ex 9.3 – 32 Questions
• Class 11 Maths Chapter 9 Ex 9.4 – 10 Questions
• Class 11 Maths Chapter 9 Miscellaneous Ex – 32 Questions

# Important Topics and Subtopics of NCERT Solutions for Class 11 Maths Chapter 9 – Sequences and Series

Topics Covered: The class 11 maths NCERT solutions chapter 9 covers the topics of arithmetic and geometric progression, arithmetic mean, geometric mean, and the relationship between them. Some special series in the form of sum to n terms of consecutive natural numbers, squares of natural numbers, and cubes of natural numbers will also be studied.

Total Questions: The class 11 maths chapter 9 Sequences and Series chapter 9 consists of a total of 74 questions, of which 45 are easy, 20 are moderate and, 9 are long answer type questions.

Listed below are the important concepts of Maths included in the Chapter 9 Sequences and Series:

• 9.1 Introduction
• 9.2 Sequences
• 9.3 Series
• 9.4 Arithmetic Progression (A.P.)
• 9.4.1 Arithmetic mean
• 9.5 Geometric Progression (G. P.)
• 9.5.1 General term of a G.P
• 9.5.2. Sum to n terms of a G.P
• 9.5.3 Geometric Mean (G.M.)
• 9.6 Relationship between A.M. and G.M.
• 9.7 Sum to n Terms of Special Series

# List of Formulas in NCERT Solutions Class 11 Maths Chapter 9 – Sequences and Series

NCERT solutions class 11 maths chapter 9 covers a lot of algebraic formulas, as the sum of sequences can also be represented algebraically. Hence, different sequences have different formulas related to them, which help in finding the sum, the nth term, or the number of terms in a sequence. Some of these important formulas covered in NCERT solutions for class 11 maths chapter 9 are given below :

• Sum of odd natural numbers : an = 2n – 1
• Fibonacci sequencean = an-2 + an-1, n>2
• Sum of first n natural numbers ; S= n(n + 1)/2
• Sum of squares of the first n natural numbers : Sn = [n(n+1)(2n+1)]/6

By a sequence, we mean an arrangement of numbers in a definite order according to some rule. Also, we define a sequence as a function whose domain is the set of natural numbers or some subsets of the type {1, 2, 3, ….k}. A sequence containing a finite number of terms is called a finite sequence. A sequence is called infinite if it is not a finite sequence.

1. Let a1, a2, a3, … be the sequence, and then the sum expressed as a1 + a2 + a3 + … is called a series. A series is called finite series if it has a finite number of terms.
2. An arithmetic progression (A.P.) is a sequence in which terms regularly increase or decrease by the same constant. This constant is called the common difference of the A.P. Usually, we denote the first term of A.P. by a, the common difference by d and the last term by l. The general term or the nth term of the A.P. is given by an = a + (n – 1) d.
3. A sequence is said to be a geometric progression or G.P., if the ratio of any term to its preceding term is the same throughout. This constant factor is called the common ratio. Usually, we denote the first term of a G.P. by a and its common ratio by r. The general or the nth term of G.P. is given by an = arn – 1

# Frequently Asked Questions (FAQs) on NCERT Solutions for Class 11 Maths Chapter 9 – Sequences and Series

Q1

### Why are NCERT Solutions class 11 Maths chapter 9 Important?

NCERT Solutions class 11 Maths chapter 9 teaches the students how to understand sequences in the most basic way possible with the help of real-world examples. Compiled by experts, the content in NCERT books is also recommended by the CBSE board, making them of utmost importance. Also, the probability of questions from these NCERT solutions coming up in the exams is high.

Q2

### Do I Need to Practice all Questions Provided in NCERT Solutions class 11 Maths Sequences and Series?

The NCERT Solutions class 11 Maths Sequences and Series requires quite a lot of formulas for finding the sum of sequences as well for finding the nth term. To memorize them, it is important for the students to practice all the solved examples as well as the exercise questions in order to solidify their learnings regarding the different kinds of progressions and thereby also increase their calculation speed.

Q3

### How Many Questions are there in NCERT Solutions class 11 Maths Chapter 9 Sequences and Series?

The NCERT Solutions class 11 Maths chapter 9 Sequences and Series has 74 questions, 45 being easy, 20 moderately easy and, 9 being of long format. They are divided among 4 exercises that target different aspects of this chapter. These cover a wide range of questions involving A.P. and G.P., thus helping the students explore the topic in detail.

Q4

### Why Should I Practice Class 11 Maths NCERT Solutions Sequences and Series chapter 9?

Q5

The NCERT Solutions class 11 Maths Sequences and Series chapter 9 are prepared by eminent scholars, and they have taken utmost care to come up with relevant content that is easily understood by all. These solutions are hence written in an easy language with relatable basic examples so as to outline the concept properly.

Q6

### What are the Important Topics Covered in NCERT Solutions class 11 Maths chapter 9?

The NCERT Solutions class 11 Maths chapter 9 explains the concept of sequences, arithmetic progression, geometric progression, Fibonacci series, the sum of special natural number sequences involving squares and cube roots. The topic of arithmetic and geometric mean through relevant logical explanation has also been covered here.

Q7

### How CBSE Students can utilize NCERT Solutions class 11 Maths chapter 9 effectively?

The students must make a habit of practicing the solved examples every day after giving a good read to the chapter. Thereafter they should start solving the exercise questions, moving gradually one section at a time to gain enough practice and confidence in all the concepts. There are formulas involved in the topic of arithmetic and geometric progression, which the students should make a note of, or they can also refer to the highlight section at the end of the chapter. In this way, the students can utilize the NCERT Solutions class 11 Maths chapter 9 effectively.

Q8

### How many sections are present in Chapter 9 of NCERT Solutions for Class 11 Maths?

The sections present in Chapter 9 of NCERT Solutions for Class 11 Maths are –
1. Introduction
2. Sequences
3. Series
4. Arithmetic Progression
5. Geometric Progression
6. Relationship between AM and GM
7. Sum to n Terms of Special Series

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