# NCERT Solutions for Class 11 Maths Chapter 9 – Sequences and Series

NCERT Solutions for Class 11 Maths Chapter 9 provide you with an easy explanation to all the questions in the exercises. All the formulae and explanations are provided with the help of examples and simplified explanations for every topic. In Chapter 9 of NCERT Solutions for Class 11, you will learn about sequences and series. This chapter is an important part of Unit Algebra which is further an important unit to prepare to score well in the CBSE exam.

The chapter consists of 4 exercises along with a miscellaneous exercise. There are a total of 96 unsolved questions in the chapter. After solving the exercises of the chapter you will understand all the important topics covered in this chapter including sequences and series, an arithmetic progression (A.P.), arithmetic mean (A. M.), geometric progression (G. P), geometric mean (G. M), the sum of ‘n’ terms of a G. P., infinite G.P and Relation between A.M and G.M.

## Important Topics for NCERT Solutions for Class 11 Maths Chapter 9

**Sequence**

The first topic of Maths NCERT Solutions for Class 11 Maths Chapters 9 sequences. A sequence is explained in the chapter as an arrangement of numbers in a definite order according to some rule. Also, it is defined as a function whose domain is a set of the natural numbers or some subset of the type (1,2,3,4……k).

**Arithmetic Progression**

One of the important topics covered in the chapter is Arithmetic Progression (A.P) which is a sequence of numbers in which each term after the first is obtained by adding a constant d to the preceding term. The constant d is called ‘common difference.’

An Arithmetic progression can be given by a, (a+d), (a+2d), (a+3d), (a+4d), …. so on. where a = first term, d = common difference.

For example, if a, b and c are in A.P, then 2b= a+c

**nth Term of an Arithmetic Progression**

The nth term of an Arithmetic Progression is explained in the chapter with the following equation:

tn=a+(n−1) d

where tn = nth term, a = first term and d = common difference

**Number of Terms of an Arithmetic Progression**

In the chapter you will also learn the formula for the nth term of an Arithmetic progression which is as mentioned below:

n = (l-a)/d +1

where n = number of terms, a = first term, l = last term and d = common difference.

**Arithmetic Mean**

If a, b and c are in A.P, then b is the Arithmetic Mean (A.M) between a and c. In this case,

b= ½ (a+c)

**Geometric Progression**

Another important topic covered in the chapter is Geometric progression, which is a sequence in which each term is derived by multiplying or dividing the preceding terms by a fixed number called the common ratio.

The general form of G.P is a, ar, ar2, ar3 and so on where ro is the common ratio and a is the scalar factor.

### Exercise-wise discussion of NCERT Solutions for Class 11 Maths Chapter 9

- The chapter consists of 4 exercises and one miscellaneous exercise.
- Exercise 9.1 consists of 14 questions based on sequences.
- Exercise 9.2 consists of questions from the topic of the arithmetic progression. There are 18 questions in the exercise.
- Exercise 9.3 consists of 32 questions from the topic of geometric mean and geometric progression
- Exercise 9.4 consists of 10 questions on the topic sum of n terms of the series.
- Miscellaneous Exercise consists of 32 questions from all the topics covered in the chapter. You must practise this exercise for being fluent with the entire topic.

### Benefits of NCERT Solutions for Class 11 Maths Chapter 9 by Instasolv

The NCERT Solutions have been prepared by highly qualified maths teachers at Instasolv which will help you address all sorts of challenging questions meticulously. The solutions are helpful not only while doing your homework but also from the CBSE examination perspective. After referring to these solutions, you will be confident enough to solve any type of questions asked during the exams. The solutions are designed after undertaking extensive research on each topic of the chapter and by keeping in mind the latest syllabus as per CBSE.