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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.

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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Frequently Asked Questions (FAQs)

1. Define AP as per Class 11 Maths chapter 9 notes.

a_1, a_2, a_3,. . . . . , a_n \text{ called an AP when the difference between }a_n and \ a_{n+1} \ is \ d

2. Define GP.

a_1, a_2, a_3,. . . . . , a_n \text{ called an AP when the difference between }a_n and \ a_{n+1} \ is \ d

3. What is the relation between AM and GM.

a_1, a_2, a_3,. . . . . , a_n \text{ called an AP when the difference between }a_n and \ a_{n+1} \ is \ d

4. Which textbook should be followed for this chapter?

NCERT Class 12 books will be a good option. In chapter 7 the sequence and series chapter is provided.

5. How can we get Class 12 chapter 7 notes as a pdf can be downloaded?

The notes for Class 12 chapter 7, sequence, and series chapter can be downloaded from the given link below

link:https://school.careers360.com/ncert/ncert-class-12th-chemistry-chapter-7-the-p-block-elements-notes

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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