CBSE NCERT Solutions For Class 11 Maths Chapter 9: According to the NCERT Class 11 Maths Chapter 9, in mathematics, the word, ‘sequence’ is used in much the same way as it is in ordinary English. When we say that a collection of objects is listed in a sequence, we usually mean that the collection is ordered in such a way that has an identifies first member, second member, third member and so on. For example, population of human beings or bacteria at different times form a sequence. The amount of money deposited in a bank, over a number of years forms a sequence.
Solving the NCERT Solutions For Class 11 Maths Chapter 9 will teach you that depreciated values of certain commodities occur in a sequence. Sequences have important applications in several spheres of human activities. CBSE NCERT Solutions for Class 11 Chapter 9 also teaches that sequences, following specific patterns, are called progressions. Besides teaching you more about A.P; arithmetic mean, geometric mean, relationship between A.M. and G.M, special series in forms of sum to n terms of consecutive natural numbers, sum to n terms of squares of natural numbers and sum to n terms of cubes of natural numbers will also be taught in the CBSE Class 11 Maths Chapter 9. Solving the Solutions for NCERT Class 11 Maths Chapter 9 will further clear any confusion you might have on this topic. We get you completely solved NCERT Solutions for Class 11 Maths Chapter 9 by the best teachers at Embibe.
NCERT Solutions For Class 11 Maths Chapter 9: Sequences And Series
The topics and sub-topics of NCERT Class 11 Maths Chapter 9 Sequences And Series will assist you in your CBSE Class 11 Maths Preparation. The topics and sub-topics of this topic will aid you in preparing well for the CBSE Exam. This will also help you in understanding the topics under NCERT Class 11 Maths Chapter 9:
| 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 |
NCERT Solutions For Class 11 Maths Chapter 9 PDF Download
Once you solve the NCERT Solutions for Class 11 Maths Chapter 9, it will be easy for you to solve various kinds of sums.
Consider the following examples:
Assume that there is a generation gap of 30 years, we are asked to find the number of ancestors, i.e., parents, grandparents, great grandparents, etc. that a person might have over 300 years. Here, the total number of generations= 300/30=10. The number of person’s ancestors for the first, second, third, tenth generations are 2,4,8,16,32,…,1024. These numbers form what we call a sequence.
According to the CBSE NCERT Class 11 Maths Chapter 9, consider the successive quotients that we obtain in the division of 10 by 3 at different steps of division. In this process we get 3,3.3,3.33,3.333,… and so on. These quotients also form a sequence. The various numbers occurring in a sequence are called its terms.
Apart from these terms, students will also get to know about terms like Geometric Mean, Arithmetic Mean, Arithmetic Progression, Series and the relationship between them. You can download the Solutions for NCERT Class 11 Maths Chapter 9 PDF along while practising the questions from this chapter. These solutions will instantly help you whenever required. Click on the link below to download Solutions of Class 11- Sequence and Series in PDF format.
Below is the sample image of the NCERT Solutions for Chapter- Sequence and Series.
NCERT Solutions For Class 11 Maths Chapter 9: Sequences And Series
We denote the terms of a sequence by a1, a2, a3,…,an,…, etc, the subscripts denote the position of the term. The nth term is the number at the nth position of the sequence and is denoted by an. The nth term is also called the general term of the sequence. Thus, the terms of the sequence of a person’s ancestors mentioned above are a1=2, a2=4, a3=8,…, a10=1024. Similarly, in the example of successive quotients a12=3.3, a3=3.33,…a6=3.33333, etc.A sequence containing a finite number of terms is called a finite sequence. For example sequence of ancestors is a finite sequence since it contains 10 terms (a fixed number). CBSE NCERT Class 11 Maths Chapter 9 Sequences and Series further teaches a sequence is called infinite, if it is not a finite sequence. For example, the sequence of successive quotients mentioned above is an infinite sequence, infinite in the sense that it never ends.
| NCERT Solutions for Class 11 Maths Chapter 1 | NCERT Solutions for Class 11 Maths Chapter 3 | NCERT Solutions for Class 11 Maths (All Chapter) |
NCERT Solutions For Class 11 Maths Chapter 9: Important Questions
We have compiled a list of important questions from the Chapter- Sequence and Series. Students can refer to these questions for quick revision.
| 1. The 5th, 8th, and 11th terms of a GP are p, q and s respectively. Prove that q2 = ps 2. Find three numbers whose product is 1728 and sum is 38. 3. Find the sum of first 30 positive integers multiple of 6. 4. Prove that the sum of n number of terms of two different AP’s can be same for one value of n. 5. Find two positive numbers m and n whose AM and GM are 34 and 16 respectively. 6. What will Rs 5000 amount to in 10 years, compounded annually at 10% per annum? |
This article on CBSE NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series will be helpful to you in clearing your doubts regarding this topic. As the questions from Sequence and Series are asked in entrance examination like JEE Main and other state CET’s, students are advised to solve as many questions as they can. Also, solve previous year papers and take a sufficient amount of mock tests. Taking free JEE Main Mock Test on Embibe will help you if you further aim to take competitive exams. The tests on Embibe are specially formulated to help you gain confidence and work on your time-management skill.
If you have any query regarding this article on NCERT Solutions for Class 11 Maths Chapter 2, do let us know about it in the comment section below and we will get back to you soon.
503 Views