RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11B) Exercise 11.2

RS Aggarwal Solutions

RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11B) Exercise 11.2

Last updated date: 18th Apr 2024

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RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression

Free PDF download of RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11B) Exercise 11.2 solved by Expert Mathematics Teachers on Vedantu. All Ex 11.2 Questions with Solutions for RS Aggarwal Class 10 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams. Every NCERT Solution is provided to make the study simple and interesting on Vedantu.

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Introduction Class 10 Chapter 11 - Arithmetic Progression (Ex 11B) Exercise 11.2

RS Aggarwal Solutions Class 10 Chapter 11 Arithmetic Progression lays down the basics of Arithmetic Progression and how to find certain terms in the progression.

What is an Arithmetic Progression?

An Arithmetic Progression is a sequence of numbers such that the difference between any two successive members of the sequence is constant. A term in an Arithmetic Progression is the number that appears in a particular position in the sequence.

The first term in an Arithmetic Progression is the smallest number in the sequence. The common difference is the constant difference between any two successive terms in the sequence.

Students can find the nth term of an Arithmetic Progression using the formula:

T_n= a + (n-1)d, where a is the first term, d is a common difference, and n is the number of terms in the sequence.

Example:

The first term in an Arithmetic Progression is 4, and the common difference is 3. Find the 5th term in the sequence.

T_n = a + (n-1)d

T_n = 4 + (5-1)3

T_n = 4 + 2*3

T_n = 4 + 6

T_n = 10

The 5th term in the sequence is 10.

Finding terms in an Arithmetic Progression:

To find a particular term in an Arithmetic Progression, you need to know the first term, the common difference and how many terms are in the sequence.

Example:

How many terms are there in an Arithmetic Progression whose first term is 4 and in which the common difference is 3?

To find this out, substitute a = 4, d = 3 and n = ? in T_n = a + (n-1)d

T_n = 4 + (n-1)d

T_n = 4 + (?-1)3

T_n = 4 + (-2)*3

T_n = 4 - 6

T_n = -2

There are two terms in the sequence. The second term is -2.

Finding the sum of an Arithmetic Progression:

To find the sum of an Arithmetic Progression, you need to know the first term, the common difference and how many terms are in the sequence.

Example:

The first term in an Arithmetic Progression is 4, and the common difference is 3. Find the sum of the first ten terms in the sequence.

To find this out, substitute a = 4, d = 3 and n = 10 in T_n = a + (n-1)d

T_n = 4 + (n-1)d

T_n = 4 + (10-1)3

T_n = 4 + 9*3

T_n = 4 + 27

T_n = 31

The sum of the first ten terms in the sequence is 31.

Sum of first n even terms:

If we want to know the sum of first n even terms, then simply double the common difference. In other words, if there are a total of n terms in an Arithmetic Progression and all the terms after the first two terms are even, then the sum of all such terms is double the common difference.

FAQs on RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression (Ex 11B) Exercise 11.2

1. What is an Arithmetic Progression?

An Arithmetic Progression is a sequence of numbers in which the difference between any two successive members of the sequence is constant. A term in an Arithmetic Progression is the number that appears in a particular position in the sequence. The first term in an Arithmetic Progression is the smallest number in the sequence. The common difference is the amount by which each successive term differs from the preceding term. Students can learn more about Arithmetic Progressions in RS Aggarwal Solutions Class 10 Chapter 11 - Arithmetic Progression. This solution will be beneficial in preparing for the CBSE Class 10 exams.

2. What is the nth term of an Arithmetic Progression?

The nth term of an Arithmetic Progression is the term that appears in the nth position in the sequence. The first term in an Arithmetic Progression is a, and the common difference is d. This can be expressed as:

T_n = a + (n - 1) d

Where Tn is the nth term, a is the first term, d is a common difference, and n is the number of terms in the sequence. Students should be aware that the subscript n is not an exponent. The solutions for RS Aggarwal Class 10 Maths Chapter 11 can help students with these terms and concepts. Vedantu offers expert online coaching for CBSE students. Our team of highly qualified and experienced mathematics teachers will help you to understand these concepts in detail.

3. What is the sum of first n terms in an Arithmetic Progression?

The sum of first n terms in an Arithmetic Progression is the total value of all the numbers in the arithmetic sequence, starting with term one and ending with term n. It can also be found by multiplying each term by its number, adding them together, and dividing the result by the common difference. This can be expressed as:

S_n = (a + d)n / 2

Where Sn is the sum of first n terms, a is the first term, d is a common difference, and n is the number of terms. Students can use this formula to help them with their exam preparation.

4. What is a geometric progression?

A geometric progression is a sequence of numbers in which each successive term differs from the preceding term by a constant multiple, called the common ratio. In a geometric sequence, if r denotes any number in terms of 'r' being taken as the common ratio, then Sx = Rsx. This can be expressed as:

Sx = Rsx

Where Sx is the sum of first n terms, Rs is the common ratio, and x is the number of terms. The solutions for RS Aggarwal Class 10 Maths Chapter 11 can help students understand geometric progressions in more detail.

5. What is the sum of first n terms in a geometric progression?

The sum of first n terms in a geometric sequence is the total value of all the numbers in the geometric sequence, starting with term 1 and ending with term n. It can also be found by multiplying each term by its number, adding them together and then dividing the result by the common ratio. This can be expressed as:

S_n = Rx(x - 1) / r

Where Sn is the sum of first n terms, x is the number of terms, Rx is the common ratio, and r is the number in terms of 'r' being taken as the common ratio. Students can use this formula to help them with their exam preparation.