RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11A) Exercise 11.1

Q: 1. What Is the Distinction Between Arithmetic and Geometric Progression mentioned in RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11A) Exercise 11?

Arithmetic ProgressionGeometric ProgressionArithmetic Progression is a set of terms in which the new term is the difference between two previous terms with the same value.Geometric progression is defined as a series in which the new term is obtained by multiplying two consecutive terms with a constant factor between them.With the help of a common difference between consecutive terms, the series is identified as an Arithmetic Progression.With the help of a common ratio between consecutive terms, the series is identified as a geometric progression.The terms that follow each other change in a linear fashion.The terms follow each other very exponentially.

Q: 3. How do you distinguish between sequences, series, and progression according to RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11A) Exercise 11?

The differences between the three are listed below.A sequence is a list of numbers that follow a specific pattern and can be finite or infinite. For example, the sequence 1, 2, 3, 4, 5,... is an infinite sequence of natural numbers.The sum of the elements in a sequence is called a series. The series of natural numbers 1+2+3+4+5... is an example. A term is a number that appears in a sequence or series.A progression is a series of events in which the general term can be expressed mathematically.Students can download the solutions and more such material from the website of Vedantu and make the best choice, thus excelling in academics.

RS Aggarwal Solutions

RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11A) Exercise 11.1

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About Arithmetic Progression

The differences between every two consecutive terms in an Arithmetic Progression (AP) are the same. It is possible to derive a formula for the nth term from an Arithmetic Progression. The sequence 3, 6, 15, 21, 27,..., for example, is an Arithmetic Progression (AP) because each number is obtained by adding 3 to the previous term. The nth term in this sequence is 6n-3. By substituting n=1,2,3,... in the nth term, you can get the sequence's terms. i.e.,

When n = 1, 6n-3 = 6(1)-3 = 6-3=3
When n = 2, 6n-3 = 6(2)-3 = 12-3=9
When n = 3, 6n-3 = 6(3)-3 = 18-3=15

What exactly is Arithmetic Progression?

An Arithmetic Progression (AP) can be defined in two ways:

An Arithmetic Progression is a series of terms with the same differences between them.
Each term is obtained by adding a fixed number to the previous term in an Arithmetic Progression, with the exception of the first.

Arithmetic Progression Terminology

First Term: The first term of an AP is the progression's first number, as the name implies. It is usually denoted by the letters a1 (or) a.

For instance, the first term in the sequence 3,9,15,21,28,... is 3, i.e. a1=3 (or) a=3.

Common Difference: We know that an AP is a sequence in which each term, except the first, is obtained by multiplying the previous term by a fixed number. The "fixed number" is known as the "common difference," and it is represented by the letter 'd.' If the first term is a1, then the second term is a1+d, the third term is a1+d+d = a1+2d, and so on. For instance, each term in the sequence 3,9,15,21,27... is obtained by adding 6 to the previous term, with the exception of the first term. As a result, d=6 is the common difference. The difference between every two consecutive terms of an AP is the most common difference. As a result, the formula for calculating an AP's common difference is d = an-a{n-1}.

Calculating the Sum of Arithmetic Progression Formula

Consider an Arithmetic Progression (AP) with a1 (or) an as the first term and d as the common difference.

Sn = n/2[2a+(n-1) d] is the sum of the first n terms of an Arithmetic Progression when the nth term is unknown.
Sn = n/2[a1+an] is the sum of the first n terms of an Arithmetic Progression when the nth term, an, is known.

FAQs on RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11A) Exercise 11.1

1. What Is the Distinction Between Arithmetic and Geometric Progression mentioned in RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11A) Exercise 11?

Arithmetic Progression	Geometric Progression
Arithmetic Progression is a set of terms in which the new term is the difference between two previous terms with the same value.	Geometric progression is defined as a series in which the new term is obtained by multiplying two consecutive terms with a constant factor between them.
With the help of a common difference between consecutive terms, the series is identified as an Arithmetic Progression.	With the help of a common ratio between consecutive terms, the series is identified as a geometric progression.
The terms that follow each other change in a linear fashion.	The terms follow each other very exponentially.

2. What are some key points to remember from RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11A) Exercise 11?

An AP is a set of numbers in which each term is obtained by multiplying the preceding number by a fixed number.
The first term is represented by a, the common difference is represented by d, the nth term is represented by an, and the number of terms is represented by n.
AP can be written as a, a+d, a+2d, a+3d, and so on.
An AP's nth term can be calculated as a = a + (n1)d.
The sum of an AP can be calculated using either sn=n/2[2a+(n1)d] or sn=n/2[2a+(n1)d].
An AP's graph is a straight line with the common difference as the slope.

3. How do you distinguish between sequences, series, and progression according to RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11A) Exercise 11?

The differences between the three are listed below.

A sequence is a list of numbers that follow a specific pattern and can be finite or infinite. For example, the sequence 1, 2, 3, 4, 5,... is an infinite sequence of natural numbers.
The sum of the elements in a sequence is called a series. The series of natural numbers 1+2+3+4+5... is an example. A term is a number that appears in a sequence or series.
A progression is a series of events in which the general term can be expressed mathematically.

Students can download the solutions and more such material from the website of Vedantu and make the best choice, thus excelling in academics.