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

NCERT Solutions for Class 11 Maths Chapter  9 Sequences and Series

By sequence we mean, the progression of numbers in a definite order. In the previous classes, we have studied about arithmetic progression(A.P). In this chapter, we will discuss more arithmetic progression(A.P) and also discuss geometric progression(G.P). There is a total of 74 questions are given in 4 exercises and for more practice, this topic 32 questions are given in a miscellaneous exercise. The NCERT Solutions for Class 11 Maths Chapter  9 Sequences and Series are designed and prepared by our subject experts. These NCERT solutions are the step-by-step explanation of NCERT textbook questions and these solutions help students in their preparation of CBSE class 11 final examination as well as in various competitive exams like JEE Main, BITSAT, VITEEE etc.

A sequence is the arrangement of numbers or terms in such a way so that we can identify the first number, second number, third number and so on according to some rule. In NCERT Class 11 Maths Chapter 9 Sequences and Series we will discuss arithmetic progression(A.P), geometric progression(G.P), arithmetic means(A.M), geometric mean(G.M), the relationship between A.M. and G.M, sum to n terms of special series special series, sum to n terms of squares and cubes of natural numbers. In NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series, we study two types of sequence - finite sequence and infinite sequence. A sequence containing a finite number of terms or in other words we can say that if the sequence has a first term and the last term, and all the terms follow a definite order is called a finite sequence. A sequence is called infinite if it is not a finite sequence.

## Important terms of NCERT Class 11 Maths Chapter  9 Sequences and Series-

• Arithmetic Progression-It is a sequence of numbers or terms, in which the terms decreases or increases by the same constant or in other words difference between the consecutive term is constant. For example in this series 4, 7, 10 13, 16…. Is an arithmetic progression(A.P) with a common difference of 3. Generally, we denote the first term in arithmetic progression(A.P) by 'a' and the common difference by 'd' .The nth term or the general term and the sum $S_n$ of the first $n$ terms of an arithmetic progression(A.P) is given by-

$\\a_n = a_1 + (n-1).d\\\:\\S_n=\frac{n}{2}[2a+(n-1).d]$

• Geometric progressions (G.P)- A sequence is said to be a G.P if the ratio of any number to its preceding number is the same throughout. This constant factor is called the common ratio of the G.P and usually, it is denoted by 'r' and the first term of a Geometric progression (G.P) is denoted by 'a'. The nth or the general and the sum $S_n$ of the first $n$ terms of G.P. is given by-

$\\a_n=ar^{n-1}\\\:\:\\ S_n=\frac{a(r^n-1)}{r-1}=\frac{a(1-r^n)}{1-r}$

## Topics of NCERT Grade 11 Maths Chapter- 9 Sequences and Series

9.1 Introduction

9.2 Sequences

9.3 Series

9.4 Arithmetic Progression (A.P.)

9.5 Geometric Progression (G.P.)

9.6 Relationship Between A.M. and G.M.

9.7 Sum to n terms of Special Series

## The complete Solutions of NCERT Class 11 Mathematics Chapter 9 is provided below:

NCERT Solutions for Class 11 Maths Chapter  9 Sequences and Series - Exercise 9.1

NCERT Solutions for Class 11 Maths Chapter  9 Sequences and Series - Exercise 9.2

NCERT Solutions for Class 11 Maths Chapter  9 Sequences and Series - Exercise 9.3

NCERT Solutions for Class 11 Maths Chapter  9 Sequences and Series - Exercise 9.4

NCERT Solutions for Class 11 Maths Chapter  9 Sequences and Series - Miscellaneous

## NCERT Solutions for Class 11 Mathematics

 Chapter-1 Sets Chapter-2 Relations and Functions Chapter-3 Trigonometric Functions Chapter-4 Principle of Mathematical Induction Chapter-5 Complex Numbers and Quadratic equations Chapter-6 Linear Inequalities Chapter-7 Permutation and Combinations Chapter-8 Binomial Theorem Chapter-10 Straight Lines Chapter-11 Conic Section Chapter-12 Introduction to Three Dimensional Geometry Chapter-13 Limits and Derivatives Chapter-14 Mathematical Reasoning Chapter-15 Statistics Chapter-16 Probability

## NCERT Solutions for Class 11- Subject wise

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