Revision Notes for ICSE Class 10 Math Chapter 11 - Free PDF Download
FAQs on ICSE Class 10 Mathematics Revision Notes Chapter 11 - Geometric Progression
1. Why do Class 10 students prefer Vedantu to study Maths Chapter 11 Geometric Progressions?
Vedantu provides the best content as far as the quality is concerned. And ICSE Maths notes for Chapter 11 Geometric Progression is no such exception. We keep in mind that all the students of Class 10 can get a better overview of the chapter through our well precise notes. In our notes, we have mentioned all the details of the concepts along with relevant derivations and formulas that promote conceptual learning. Moreover, we ensure that we deliver all the important information in a concise form, so students may not overload their brains with extra details.
2. What is a geometric progression?
A geometric progression is a special type of progression in which the successive terms or numbers have a constant ratio. Here, the constant ratio is also known as a common ratio. Geometric progression is known as GP. And is represented in the form of a, ar, ar^2, ar^3, where a is the first term, and r is the constant ratio of the progression. A common ratio can have both positive and negative values. Students can find GP if they know the common ratio and the first term.
3. How many types of geometric progressions are there?
There are two types of geometric progressions. The types of geometric progressions in a progression series are based on the number of terms present in the series. The types of geometric progressions are infinite geometric progressions and finite geometric progressions.
Finite Geometric Progression- It is a geometric series that consists of a finite number of terms. In this progression, the last term is already defined. For example 1/3, 1/6, 1/12 to 1/96. Here, the last term 1/96 is predefined.
Infinite Geometric Progression- It contains an infinite number of terms. Here, the last term is not defined. Example- 3, -5, 10 is an infinite series where the last term is not predefined.
4. What is a geometric progression formula?
A geometric progression formula is used to find the nth term in a number series or progression. The nth term can only be calculated if the common ratio and the first term is known. If the common or constant ratio is not known, it can be calculated by dividing the term by its preceding term. The formula for finding the nth term of a GP is given as- an= ar^n-1. Here, a is the first term, n is the number of the term to be calculated, and r is the common ratio.
5. What is the geometric progression sum formula?
The geometric progression sum formula is used to find the sum of all the terms present in the series. The sum of the terms in the geometric progression can be calculated by two methods. The formula used is different for finite and infinite GP series.
For Finite GP
In a finite GP, the sum of the terms is calculated by the formula, sn= a(1-r^n)/(1-r) for r not equal to 1. And Sn= an, for r=1.
For Infinite GP
In an infinite GP, the sum of the terms is calculated by the formula, S infinite= a/(1-r), where r is the common ratio less than 1. And a is the first term. In the case of r>1, the sum can't be calculated.