# RS Aggarwal Class 11 Chapter 12 Solutions (Geometrical Progression)

RS Aggarwal Solutions for Class 11 Maths Chapter 12 are created by the best subject matter experts at Instasolv so that you can revise the chapter quickly. RS Aggarwal Class 11 Solutions for Maths subject is highly recommended by many teachers as it contains ample questions for practice. But you might require help at certain times in solving these questions. This where our solutions will help you.

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

RS Aggarwal Solutions for Chapter 12 Class 11 Maths By Instasolv is going to help you in all ways when you are not able to find the right solutions. The solutions are provided to you in a simplified manner that you can easily grasp each concept of the chapter. Once, you have a complete understanding of the concepts, you won’t face any further issues in the question paper.

## Important Topics for RS Aggarwal Solutions for Class 11 Maths Chapter 12

**Geometrical Progression**

In mathematics, a geometric progression referred to as a geometric sequence. It is a sequence of numbers where each term after the first is a result of multiplying the previous number by a fixed non zero number. For example, sequence 3, 9, 27,…. Is a geometric progression with common ratio 3.

**The general form of a Geometrical Progression **

The general form of a G.P. is a_{1}, a_{1}r, a_{1}r^{2}, a_{1}r^{3}, a_{1}r^{n-1}, a_{1}r^{n-1}

**What is a general (nth) term of a GP?**

For example, the different terms of a geometric progression are a_{1}, a_{2}, a_{3}, a_{m}, …… a_{n}.

All these terms, according to the first term, give us,

a_{1} = a_{1}

a_{2}= a_{1}r

a_{3}= a_{2}r = (a_{1}r)r = a_{1}r^{2}

a_{n}= a_{1}r^{n-1}

**The common ratio of a GP**

You get the common ratio of geometric progression by dividing any term by the preceding term: r = a_{2} / a_{1}

**What is the sum of first n terms of a geometric progression?**

To calculate the sum of first n term of a GP we use the following formula:

S_{n}= a_{1}(1- r^{n}) / (1-r )

Where r = 1. Here n is the number of terms, a_{1} is the first term and r is the common ratio.

**Properties of Geometric Progression**

Below listed are the different properties of a Geometric Progression:

- If you multiply or divide a constant non zero term to each and every term of a G.P, then the resulting termination of the sequence is also in Geometrical Progression with a common difference.
- In G.P, the reciprocal of all the terms in G.P, eventually form a GP.
- If all the terms in G.P are raised to the same power then the new series are also in G.P.
- Three non-zero terms x, y, and z are in G.P if y
^{2}= xz.

**Other Things you will learn in the chapter are:**

- The common term of a GP
- Finite and Infinite Geometric Progression
- Sum of n terms of a GP
- Different examples based on different topics

## Exercise-Wise Discussion RS Aggarwal Solutions for Class 11 Maths Chapter 12

**Exercise 12A**

This exercise 12A has 18 questions in which you have to prove different situations asked in the questions, different number of terms and product of terms of a GP.

**Exercise 12C**

This exercise 12C has 16 questions in which you have to find the common ratio, the sum of n terms of GP, a single term say 10th term of a GP and sum of geometric series.

**Exercise 12D**

This exercise 12D has 6 questions.

**Exercise 12E**

This exercise 12E has 10 questions in which you have to find different numbers of the GP, find values for x or k and prove different situations.

**Exercise 12F**

This exercise 12F has 9 Questions in which you have to find geometric and arithmetic mean in different questions

**Exercise 12G**

This exercise 12G has 13 questions in which you have to find, common ratio, write different values in a simple function, find a rational number, prove different situations, the sum of infinite series etc.

**Exercise 12H**

This exercise 12H has 13 questions like finding the common ratio, the number of terms, finding the sum of the first five terms of a GP, expressing ‘a’ as a rational number etc.

## Benefits Of RS Aggarwal Solutions for Class 11 Maths Chapter 12 by Instasolv

If you are a student of class 11 and do not want to struggle anymore in finding the solutions to the questions given in RS Aggarwal book, then you can choose the RS Aggarwal Class 11 Maths Solutions for Chapter 12. All the solutions are designed in a manner so that you can easily understand all the concepts properly. The subject matter experts make the entire chapter content easy for you by giving a detailed explanation of every topic to you.