NCERT Solutions for Class 11 Maths Exercise 9.4

AM – the Arithmetic Mean and Geometric Mean (G. M.) are the next and most important topic in the chapter 9 sequence. Using the PDF and video solutions of 11th Mathematics Exercise 9.4, you will learn that geometry mean is the nth root of the product. Here n represents and number present in the sequence. Exercise 9.4 contains 10 questions based on Special Series. These are sum of n terms, sum of squares of n terms and sum of cubes of n terms. The specific formula for the calculation of all type of sum are given here.

Before starting the exercise, you may understand it with the illustration given below. In a sequence of non-negative numbers a and b, there are infinite numbers. You may be able to add G₁, G₂, G₃, G₄…Gn between any two numbers.

This type of series is also a G.P. This is the generalization of the geometry mean. To understand the work of this sequence you must look into the function and example 17. Questions given in NCERT Exercise 9.4 are simple to solve after identifying the general term.

In exercise 9.4 of 11th Maths, there are only 10 questions. Out of these, questions 4 to 7 are little bit difficult to identify the general term and solve. The rest questions are direct application of sum of the special series by using formula. The geometric mean is used to calculate the compounding that is occurring from time to time. It informs the central action of the progression by taking the mean of geometric progression. It helps us to understand and analyze the fraction growth of many things.

Here, Arithmetic mean and Geometry means are two different concepts under one topic. To understand it in the simpler terms you can read the verbal illustration below. For say, you have two non-negative integers a and b, if you add another number say G in between then you will get the sequence a G b. Similarly, the geometric mean is the geometric average of two numbers.

If we have two numbers then we will multiply the number. After that take the square root of it in simple terms. These are the definition that one should keep in mind while understanding the formulae and process given below. A.M. = a + b / 2 and G.M = under root ab (√ab)