RD Sharma Class 11 Solutions Chapter 20 - Geometric Progressions (Ex 20.2) Exercise 20.2 - Free PDF
FAQs on RD Sharma Class 11 Solutions Chapter 20 - Geometric Progressions (Ex 20.2) Exercise 20.2
1. What is Geometric Progressions?
Geometric Progressions is a form of mathematical pattern in a sequence of numbers or elements. In this particular kind of sequence, the numbers are obtained by multiplying the previous number by a constant, which is called the common ratio.
Let's take an example to understand this better.
In a sequence of (1, 3, 9, 27, 81), you can tell there's a pattern. The pattern here is that, beginning from the first number, all the subsequent numbers have been obtained by multiplying the preceding number by 3. So 1×3=3, 3×3=9, 9×3=27, etc. So in this case, the common ratio is 3, which is denoted as r = 3. For more such examples download free PDF from the Vedantu website.
2. What are some of the formulas related to Geometric Progressions?
There are three main formulas used to answer questions on Geometric Progressions. The first formula is to find the "nth" term in a series of elements. The second is to derive the common ratio of a series. The last one is for the geometric progression sum. These are listed below:
Nth term: The usual form of Geometric Progressions is a1, a1r, a1r², a1r³,.... a1rn-1, a1rn
We can represent each term as a1, a2, a3, etc.
a1 = a1
a2 = a1r
a3 = a2r = (a1r) r = a1r2
And so on.
Therefore, the nth term will be
an = a1rn-1
Common Ratio: To get the common ratio, you have to divide any number in the sequence by its preceding number.
r = a2/a1
Geometric Progression Sum
Sn = a1 (1-rn)/1-r
In this, r ≠ 1
3. What are the properties of Geometric Progressions?
There are seven main properties of Geometric Progressions. These are explained below:
If any number in a Geometric Progression is multiplied or divided by the same quantity (non-zero quantity), it forms a new series of Geometric Progressions with the same common ratio.
The reciprocals of the terms in a geometric progression also form a geometric progression.
If all of the terms in a geometric progression are raised to the same power, then the new numbers also form a geometric progression.
The product of the terms equidistant from the beginning and end of a geometric progression are the same. It is also equal to the product of the first and last term.
b² = ac. This means that the non-zero quantities a, b, and c, are in a geometric progression only if b² = ac.
If the terms of a geometric progression are selected at certain intervals, the new series obtained is also a geometric progression.
The logarithm of each term in a geometric progression with non-zero, non-negative terms forms an arithmetic progression (and vice versa).
4. Is the RD Sharma Class 11 Solutions Chapter 20 - Geometric Progressions (Ex 20.2) Exercise 20.2 - PDF free to download?
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5. Why should I download the RD Sharma Class 11 Solutions Chapter 20 - Geometric Progressions (Ex 20.2) Exercise 20.2 - Free PDF?
You may wonder why the RD Sharma Class 11 Solutions Chapter 20 Geometric Progressions (Ex 20.2) Exercise 20.2 PDF is being made available for free. After all, won't people just copy the solutions and then forget about them? However, if you use these documents properly, they can actually help you learn quicker. The solutions have been broken down into step-by-step instructions to help you grasp the subject better. Therefore, the solutions to exercise 20.2 from chapter 39 Geometric Progressions has been provided by Vedantu to assist students in learning how to answer questions in their textbooks. Students can discover where they need to improve and get expert advice in tackling Geometric Progressions questions by referring to the RD Sharma Chapter 20 Exercise 20.2 Solutions PDF.