NCERT Class 11 maths chapter 9 solutions enable the students to understand the concepts of Sequence and Series & they will learn about Arithmetic Progression (A. P.) and Geometric Progression (G.P.).
Solutions for class 11 Maths chapter 9 assist the students to develop a thorough understanding of the topics explained in the Chapter Sequences and Series. The students can learn new methods of solving a particular problem in expeditious time to improve their performance in the final exam.
They can easily download class 11 Maths chapter 9 PDF solutions and study anywhere & any time.
NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series
Class 11 maths chapter 9 solutions are prepared by subject experts after undertaking extensive research on each question and their problem-solving method. Students will be able to measure their ability and improve their skills. NCERT solutions for class 11 maths chapter 9 are provided in an easy and self-explanatory way that assists the students to understand the basic and fundamental rules.
You can download CBSE NCERT Solutions for Class 11 Maths Chapter 9 Sequences and Series from below.
What will you learn in CBSE Class 11 Maths Chapter 9 Sequences and Series?
There are four exercises along with a miscellaneous exercise that assists the students to understand the concepts related to Sequences and Series clearly.
The major concepts of Maths covered in solutions for class 11 maths chapter 9 are:
9.1 Introduction: There are some important applications that student will study about the specific patterns which are the progression.
9.2 Sequences: The student will study different sequences such as finite and infinite with examples.
9.3 Series: The student will study series which is a specific type of sequence and it may also be finite and infinite like.
9.4 Arithmetic Progression (A.P.): It is a specific type of series in which two successive terms are having the same common difference onwards. The student will study about Arithmetic Mean.
9.5 Geometric Progression (G. P.): It is a specific type of series in which two successive terms are having the same common ratio onwards. The student will study about General term of a G.P, sum to n terms of a G.P, Geometric Mean (G.M.)
9.6 Relationship between A.M. and G.M.: In this type of relationship between AM and GM will assist the student to find anyone of them if another one is given.
9.7 Sum to n Terms of Special Series: The student will study some special series such as natural numbers, square of natural numbers, the cube of natural numbers, & more.
- Exercise 9.1 solutions
- Exercise 9.2 solutions
- Exercise 9.3 solutions
- Exercise 9.4 solutions
- Miscellaneous exercise solutions
Theorems and formulas used in chapter
- Let a1, a2, a3, … be the sequence, the sum expressed as a1 + a2 + a3 + … is called series.
- An (A.P) arithmetic progression is a sequence in which terms increase or decrease regularly by the same constant. The first term of A.P. denotes by ‘a’, the common difference by ‘d’ and the last term by ‘l’. The general term or the nth term of arithmetic progression is given by an = a + (n – 1) d.
- A sequence is said to be a geometric progression or G.P (Geometric Progression) if the ratio of any term to its preceding term is same throughout. The first term of a G.P. denotes by ‘a’ and its common ratio by ‘r’. The general or the nth term of Geometric Progression is given by an = arn – 1
- If three terms of A.P. are to be taken then a – d, a, a + d.
- If four terms of A.P. are to be taken then a – 3d, a – d, a + d, a + 3d.
- If five terms of A.P are to be taken, then a – 2d, a – d, a, a + d, a + 2d.
- If a, b, c are in A.P. then 2b = a + c.
- If a, b, c are in G.P. then b² = ac.
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