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 identified 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.
Referring to the NCERT Solutions For Class 11 Maths Chapter 9 will help you in your preparation. 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. You will learn about A.P. or arithmetic progressions, arithmetic mean, geometric mean, the relationship between A.M. and G.M, special series in forms of the 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, etc. Solutions for NCERT Class 11 Maths Chapter 9 will further clarify any confusion you might have on these topicc. We get you completely solved NCERT Solutions for Class 11 Maths Chapter 9 by the best teachers at Embibe.
CBSE 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 are as under:
| 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 (Class 11 Maths Ch 9 Solutions PDF), 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 and 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 from below. These solutions will instantly help you whenever required. Click on the link below to download Solutions of Class 11- Sequence and Series PDF.
Below is the sample image of the NCERT Solutions for chapter – Sequence and Series:
CBSE 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. 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 about the infinite 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 8 | NCERT Solutions for Class 11 Maths Chapter 10 | 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? |
Frequently Asked Questions On Sequence And Series Class 11 Solutions PDF
Here are some of the frequently asked questions on NCERT Solutions for Class 11 Maths Chapter 9 PDF download and their answers:
Q1. Is NCERT enough for Class 11 exams?
A. If you finish the NCERT Class 11 books thoroughly, you will definitely score well in Class 11 exams. But for exams like JEE Main, NEET, etc., you have to refer to other advanced books as well.
Q2. From where can I download CBSE 11th Maths Ch 9 Solutions?
A. You can download the NCERT solutions from Embibe.
Q3. Are the NCERT Solutions by Embibe available for free?
A. All NCERT Solutions provided by Embibe can be downloaded for free, without any signup or registration.
This article on CBSE NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series will be helpful to you in clearing your doubts. As the questions from Sequence and Series are asked in entrance examinations like JEE Main and other state CETs, students are advised to solve as many questions as they can. Also, solve previous year papers and take a sufficient amount of mock tests.
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