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Sequences And Series Class 11th Notes - Free NCERT Class 11 Maths Chapter 9 notes - Download PDF

Sequences And Series Class 11th Notes - Free NCERT Class 11 Maths Chapter 9 notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 22, 2022 04:56 PM IST

NCERT notes for Class 11 Maths chapter 9 is basically based on sequence and series. In sequence and series Class 11 notes include different formulas and derivations of the formulas. The NCERT Class 11 Maths chapter 9 notes are entirely based on the useful topics of the series and sequence. Class 11 Math chapter 9 notes are detailed and compact.

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This Story also Contains
  1. NCERT Class 11 Maths Chapter 9 Notes
  2. Arithmetic Progression (A.P)
  3. Geometric Progression (G.P)
  4. Sum To n Terms Of Special Series
  5. Significance of NCERT Class 11 Math Chapter 9 Notes
  6. NCERT Class 11 Notes Chapter Wise.

A Class 11 Maths chapter 9 note helps a student to revise before the exam. Notes for Class 11 Maths chapter 9 contains Arithmetic progression, geometric progression, arithmetic mean, geometric mean and the relation between the arithmetic mean and geometric mean. NCERT Notes for Class 11 Maths chapter 9 not only covers the NCERT and CBSE Class 11 Maths chapter 9 notes it also helps to prepare for different competitive exams.

After going through Class 11 Sequence and Series notes

Students can also refer to,

NCERT Class 11 Maths Chapter 9 Notes

Sequence

The general definition goes by arranging something in a particular order.

Generally, we write the terms of a sequence by, a_1, a_2, a_3, . . . . . . . . .a_n, . . . . . . .etc., the subscripts define the position of the term. The nth term defines the nth position of the sequence.

From the above sentences, we can say a function whose domain is the set of natural numbers or a subset of it can be defined as a sequence. A functional notation can be used for 1647336013450is a(n)

Series

Let a_1, a_2, a_3, . . . . . . . . .a_n, . . . . . . ., be a given sequence. Then, the expression

a_1+a_2+ a_3+ . . . . . . . . +a_nis known as a series

The sum of the following series is denoted by ∑a_n is a(n)

Arithmetic Progression (A.P)

Let the sequence be

\\ a_1, a_2, a_3,. . . . . . a_n \text{ called an AP when the difference between}\ a_n \ and \ a_n+1 \ is \ d \\ Thus \ a_n \ \text{can be written as } a_n=a+(n-1) d \\ \text{Let the sequence } a_1+a_2+ . . . . . +a_n \\ \text{ Then the summation is } S_n=(\frac{n}{2})[2a+(n-1)d]

Example:

If the 1,5,9,13… sequence is an A.P, what will be the nth term in the sequence?

Solution:

Given, sequence 1,5,9,13 . . . . . . .

Difference between the numbers, d =1647337241701

The nth term will be,

1647337242156

Arithmetic Mean

If the two given numbers are p and q. Insert the number F between p and q so that p,F,q are in arithmetic progression. If F be arithmetic mean of p and q numbers. Then we will have,

1647337325045

Geometric Progression (G.P)

Let us consider the following sequences:

2, 4, 8, 16, .…..

1/9, -1/27, 1/81, -1/243, ......

Let the sequence be a_1, a_2, a_3,.......a_n called a GP when the difference in the ratio between a_n \ and \ a_{n+1} \ is \ r \ by \ letting \ a_1 \ = \ a,\ \text{ we obtain a geometric progression }, a, ar, ar^2, ar^3,......

General Term Of A G.P

\\ \text{The general term of GP is } a_n= ar^{n-1} \\ \text{Sum to n terms of a G.P} \\ S_n = a + ar + ar^2 +.......+ ar^{n-1} \\ S_n=a \frac {(1-r^n)}{(1-r )}

Geometric Mean (G.M.)

The formula for GM is

G=√ab

Relationship Between A.M. and G.M

A=(a+b)/2 and G=√ab

The relation is A≥G

Sum To n Terms Of Special Series

\\ 1 + 2 + 3 + . . . . . + n \ \ \ \ \ \text{(sum of first n natural numbers)} \\ k = \frac{n(n+1)}{2} \\ \\ 1^2 + 2^2 + 3^2 +. . . . .+ n^2 \ \ \ \text{(sum of squares of the first n natural numbers)} \\ k = \frac{n(n+1)(2n+1)}{6} \\ \\ 1^3 + 2^3 + 3^3 +. . . . . . . +n^3 \ \ \ \text{(sum of cubes of the first n natural numbers)} \\ k = \left [ \frac{n(n+1)}{2} \right ]^2

The solution of this chapter can be directly solved by applying the formulas given above.

Significance of NCERT Class 11 Math Chapter 9 Notes

Class 11 Sequence and series notes cover all important topics of the chapter. Class 11 CBSE Maths Syllabus is similar to Class 11 Math chapter 9 notes. So, it will help students to get a detailed and compact knowledge of the chapter. Students will get the hard copy in the Class 11 Maths chapter 9 notes pdf download.

NCERT Class 11 Notes Chapter Wise.

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