If the ratio of two consecutive terms is always a constant quantity, a set of non-zero numbers is called a geometric progression. It is a progression of the chapter based on the Arithmetic Progression. A geometric progression is a series that progresses by the multiplication of a certain number into its previous term. The students will learn about some of the most significant qualities of a GP in this chapter:
GP's general term or nth term is a an =arn-1
if an is the initial term and r is the common ratio. a n = L/(r(n-1)) is the n th term of a GP from the end, and the L is the last term.
If all the terms in a Geometric Progression are multiplied or divided by the same non-zero constant, then the resulting sequence is a GP with the same common ratio. A sequence made up of the reciprocal terms of a GP also forms a GP, and the common ratio is the reciprocal of the previous common ratio. If a, b, and c are three consecutive terms in a GP, then b 2 = ac. G is known as the geometric mean of a and b and may be computed as G = √ab if a, G, and b are in GP. The Geometric Mean is followed by the sum of n terms of a GP. The sum of a GP = (a(1 – rn))/(1-r)
This chapter includes the important concepts of the definition of a geometric progression, how to choose terms of a GP, three terms in a GP. The sum of a finite and an infinite GP is also covered by the chapter, along with the properties of the geometric progression. The chapter also covers the topic of geometric mean, its significance and applications.
Our subject experts have written this chapter in a very simple manner to help students better understand the principles and strategies involved in solving problems within a shorter time. This is sure to increase their confidence. Students who want to achieve a high academic score in their board exams will benefit greatly from RD Sharma Class 11 Maths Solutions.