# RS Aggarwal Class 11 Solutions Chapter 12

## RS Aggarwal Solutions for Class 11 Chapter 12 – Geometrical Progression PDF

### RS Aggarwal Class 11 Solutions Chapter-wise – Free PDF Download

The Document for RS Aggarwal Class 11 Solutions Chapter 12 has easy-to-understand answers to the different kinds of questions that can be asked from the chapter. The ideas of arithmetic progression are already known to students, and the ideas of geometric progression just build on them. The chapter is worth a lot of points, and it’s best to study it well because it’s part of Unit 2-Algebra, which has the most weight on exams. Our subject experts at Utopper made the RS Aggarwal Class 11 Solutions Chapter 12 PDF. Students can clear up any questions with the RS Aggarwal Solutions for Class 11 GP.

In the RS Aggarwal Book for Class 11, Chapter 12 has about 8 exercises with almost 90 questions. All of the questions are based on the latest CBSE exam pattern as well as the JEE, NEET, and other competitive exam patterns. The chapter talks about things like geometrical progression, the nth term from the end of GP, problems with GP, word problems with GP, geometric mean, infinite geometric series, etc.

When you can’t find the right answers, RS Aggarwal Solutions for Class 11 Chapter 12 of Maths by Utopper will help you in every way. The answers are given to you in an easy-to-understand way so that you can easily understand each idea in the chapter. As soon as you fully understand the ideas, you won’t have any more problems with the question paper.

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**RS Aggarwal Class 11 Solutions Chapter 12 – Geometrical Progression **

**RS Aggarwal Class 11 Solutions Chapter 12 – Geometrical Progression**

#### RS Aggarwal Class 11 Solutions Chapter 12 Geometrical Progression – Free PDF Download

Students can use the PDF to get their ideas about geometric progressions ready. Students are tested on how well they understand and can use the ideas taught in the chapter geometric progression. The concepts are talked about in depth, and all of the questions in the PDF are answered to help you understand them better. Students should practise answering different kinds of questions. This will help them feel more at ease when they have to answer questions on tests. Here you can get the PDF for RS Aggarwal Class 11 Maths Chapter 12 Solutions.

**RS Aggarwal Class 11 Solutions**

## Chapter 1: Sets

## Chapter 2: Relations

## Chapter 3: Functions

## Chapter 4: Principle of Mathematical Induction

## Chapter 5: Complex Numbers and Quadratic Equations

## Chapter 6: Linear Equations in One Variable

## Chapter 7: Linear Equations in Two Variable

## Chapter 8: Permutations

## Chapter 9: Combinations

## Chapter 10: Binomial Theorem

## Chapter 11: Arithmetic Progression

## Chapter 12: Geometrical Progression

## Chapter 13: Some Special Series

## Chapter 14: Measurement of Angles

## Chapter 15: Trigonometric or Circular Functions

## Chapter 16: Conditional Identities Involving the Angles of a Triangles

## Chapter 17: Trigonometric Equations

## Chapter 18: Solution of Triangles

## Chapter 19: Graphs of Trigonometric Functions

## Chapter 20: Straight Lines

## Chapter 21: Circles

## Chapter 22: Parabola

## Chapter 23: Ellipse

## Chapter 24: Hyperbola

## Chapter 25: Applications of Conic Sections

## Chapter 26: Three Dimensional Geometry

## Chapter 27: Limits

## Chapter 28: Differentiation

## Chapter 29: Mathematical Reasoning

## Chapter 30: Statistics

## Chapter 31: Probability

#### Geometrical Progression

A geometric sequence is another name for a geometric progression. It is a series of numbers where each number after the first is the result of multiplying the number before it by a fixed number that is not zero. For example, sequence 3, 9, 27,…. Is a geometric sequence with the same ratio of 3

#### What is the general form of a Geometrical Progression ?

A G.P. is usually written as a1, a1r, a1r2, a1r3, a1rn-1, and a1rn-1.

What is a GP’s general (nth) term?

a, ar, ar², ar³, …..arⁿ⁻¹, arⁿ⁻¹.

- Common ratio : r = a2/a1
- The nth term of a GP: an= a1rn-1
- The sum of a GP: Sn= a1(1- rn) / (1-r )

##### Geometric Progression has these Properties:

- If you multiply or divide each part of a geometric progression by a number that is not zero, the new sequence is also a geometric progression with the same common ratio.
- All of the terms in a geometric progression can be rearranged to form another geometric progression.
- If all the numbers in a geometric progression are raised to the same power, the new sequence is also a geometric progression.
- If the following are true for any three non-zero terms, then those three terms are in a GP.
- If y2 = xz, then x, y, and z are all in the same order.

## FAQ ( Frequently Asked Questions )

**1. What are some basic Geometric Progression formulas?**

Ans – Geometric progressions are a list of non-zero numbers where the ratio between each pair of numbers stays the same. Each part of the sequence is made by multiplying the previous part by a constant called the “Common ratio” and adding that to the previous part.

The ratio that stays the same in a geometric progression is:

r = a2/a1

For the nth term of a GP, the formula is: a = a1rn-1, where an is the first term in the GP and r is the common ratio.

The formula for the sum of a GP is: Sn=a1(1-rn)/(1-r), where an is the first term, r is the common ratio, and n is the number of terms.

**2. What are the subtopics that the PDF goes into more depth about?**

Ans – There are a lot of ideas about Geometric progressions in this chapter. There are some basic ideas and some topics that are more about how to use them. A geometric progression is a list of numbers where the ratio between each pair of numbers is about the same. Download the free PDF from this page to learn more about each of the ideas.

The RS Aggarwal Class 11 Maths Geometrical Progression PDF goes into detail about the following:

- The general term of a GP
- Selection of terms of GP
- The Sum of a GP
- Sum of an infinite GP
- Properties of geometric progressions
- Properties of arithmetic and geometric means
- Insertion of geometric mean between two numbers

**3. How do I get the RS Aggarwal Class 11 Solutions Chapter 12?**

Ans – Students should go to the Utopper website or app to get the answers to Chapter 12 Geometric Progression from RS Aggarwal for Class 11. Students can get the best free study materials from Utopper, which they can use online or off, whenever it’s most convenient for them. These solutions from Utopper are put together by experts in the field who make them fit the needs of the students. Students can get to the RS Aggarwal solutions by going to the Utopper website and clicking on the Class 11 tab under RS Aggarwal under the “Solutions for popular reference solutions” tab. User can also get access free study materials like Revision Notes, Important Questions and many more.