NCERT Exemplar Class 11 Maths Chapter 9 Solutions: Sequences and Series
NCERT Exemplar Solutions for Class 11 Maths Chapter 9 deal with arithmetic and geometric progression. The solutions for this chapter of NCERT Exemplar Class 11 Maths are prepared by the expert maths teachers at Instasolv with an aim to provide a fundamental aspect of mathematics to you for class 11. The Exemplar solutions are a major reference guide to help you score well in the class 11 CBSE exams as well as the entrance exams.
Some of the main topics of this NCERT Exemplar Class 11 Maths Solutions Chapter 9 are Sequences, Series, Arithmetic Progression, Geometric Progression, Arithmetic Mean, Geometric Mean, and Relationship between Arithmetic Mean and Geometric Mean. Practising the questions based on these topics will help you clear your concepts on the Arithmetic Progression and Geometric Progression.
Chapter 9 – Sequences and Series contains 4 main exercises with a total of 57 questions. Solving these exercise wise problems daily will help you improve your problem-solving skills, which are essential to achieve a better academic score. Following the solutions provided by Instasolv will help you in a better understanding of the chapter.
Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 9 – Sequences and Series
A function whose domain is the set N of natural numbers is called the sequence whereas a sequence whose range is a subset of R is known as a real sequence. For example, the population of human beings several times, the amount of money left in a bank, etc.
Let p1, p2, p3, p4, … be the sequence, then the sum represented as p1 + p2 + p3 + p4 + … is known as series. A series is termed as the finite series if it has a finite number of terms.
An arithmetic progression is a sequence in which terms rise or fall regularly by the same constant. This constant is known as the common difference of the arithmetic progression. Generally, we represent the first term of arithmetic progression by ‘p’, the common difference by ‘d’ and the last term by ‘l’. The general term or the nth term of the arithmetic progression is given by pn = p + (n – 1) d.
A geometric progression is the sequence of non-zero numbers if the ratio of each term, excluding the first one, by its previous term is always the same. , p, pr, pr2, ………, prn-1, …., where a is the first term and r is the common ratio.
Important Formulas of Sequences and Series
- To get the nth term of the arithmetic progression
pn = p + (n-1)d
- To find the sum of first n terms of an arithmetic progression
Sn = n/2. [2p + (n-1)d] = n/2. (p+l)
- The arithmetic mean of two numbers p and q = (p + q)/ 2
- To find the sum of first n terms of a geometric progression
Sn = p (rn – 1)/ (r-1) or p (1 – rn)/ (1 – r), if r ≠ 1
- The geometric means of any two positive numbers p and q = √pq, where p, G, q is a geometric progression.
Exercise-wise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 9 – Sequences and Series
Exercise 9.1 – Short Answer Type Questions
In this exercise of Chapter 9 – Sequences and Series there are a total of 12 questions that are based on the concepts of Arithmetic Progression and Geometric Progression.
Exercise 9.2 – Long Answer Type Questions
NCERT Exemplar Class 11 Chapter 9 Exercise 9.2 contains a total of 4 questions. They are long answer type questions where you have to find the arithmetic mean and geometric mean. There are also questions related to the relationship between arithmetic mean and geometric mean.
Exercise 9.3 – Objective Type Questions
This exercise consists of a total of 20 questions which are objective type questions based on arithmetic progression and geometric progression. In these questions, you will be provided with 4 options and you have to choose the right answer.
Exercise 9.4 – Very Short Answer Type Questions
Exercise 9.4 consists of very short answer type questions including match the following, fill in the blanks, and state true or false. Solving these questions will help you have prepared for the competitive exams as well.
Why Use NCERT Maths Exemplar Solutions Class 11 Chapter 9 – Sequences and Series by Instasolv?
- The NCERT Exemplar Solutions Class 11 Maths Chapter 9 helps you in scoring high marks in the CBSE exam.
- The solutions are developed by qualified experts who are well-versed with the different techniques of teaching maths concepts in class 11.
- All the solutions are based on the latest syllabus released by NCERT and majorly cover all the topics of the chapters in a well-structured format.
- Covering all the important topics of the chapters in systemic order is one of the major benefits this NCERT Exemplar Class 11 Maths Solutions Chapter 9 provides to you.
Follow the NCERT Exemplar solutions provided by Instasolv now to excel in your exams!