RD Sharma Class 11 Solutions Chapter 20 - Geometric Progressions (Ex 20.5) Exercise 20.5

Twenty pupils will benefit from the in-depth explanations in the RD Sharma Exercise 20.5 Class 11 Chapter. The properties of geometric progressions and geometric series are the major topics on which students should concentrate. Students will be able to grasp the fundamental principles of Geometric Progressions if they pay close attention to each component of Chapter 20.5 RD Sharma Solutions.

RD Sharma Solutions for Class 11 Math Chapter 20

In the RD Sharma Chapter 20 solutions, the professionals have come up with a variety of solutions. Some students struggle when attempting difficult questions from Geometric Progressions, which is why the professionals have offered the appropriate resources. 

When students look over the material of Solutions Chapter 20, they will be able to better prepare themselves.

The pupils will be able to overcome all of the obstacles in Geometric Progressions.

All of the components that belong under RD Sharma Geometric Progressions have been thoroughly explained with appropriate visuals, and if you carefully analyze the material, you will have no questions.

The beauty of following solutions is that you will receive fresh ideas for improving your preparation procedures. Chapter 20 of CBSE Class 11

Example: 1 Prove that log a, log b, and log c are in A.P. if a, b, and c are in G.P.

Solution:

It is given that a, b and c are in G.P.

b2 = ac {using property of geometric mean}

(b2)n = (ac)n

b2n = an cn

Now, apply log on both the sides we get,

log b2n = log (ancn)

log (bn)2 = log an + log cn

2 log bn = log an + log cn

∴ log an, log bn, log cn are in A.P

Example: 2 Prove that 1/loga m, 1/logb m, and 1/logic m are in A.P. if a, b, and c are in G.P.

Solution:

Given:

a, b and c are in GP

b2 = ac {property of geometric mean}

Apply log on both sides with base m

logm b2 = logm ac

logm b2 = logm a + logm c {using property of log}

2logm b = logm a + logm c

2/logb m = 1/loga m + 1/logc m

∴ 1/loga m , 1/logb m, 1/logc m are in A.P.