Geometric Progression is one of the favorite chapters and topics of the students who are in the maths stream. The geometric Progression or the geometric sequence is the number sequence where each term multiplies with the previous one with a fixed number other than zero. This making of the chain is known as the common ratio.
One can take the example of the following. 3, 6, 12, 24, 48… is a geometric progression too. In this sequence, the common ratio is 2.
The geometric sequences can have the power of a non-zero digit, which is a fixed number, for example, 4n or 5n. The geometric sequence can be described as a, ar, ar2,ar3.… where the r is not equal to zero and is also the common ratio. The a is the scale factor, which is also equal to the starting value of the whole sequence.
But is learning the Geometric series important? The geometric series helps us to solves quizzes, which is related to numbers and patterns in a sequence. The questions of the geometric series often come in prestigious exams such as the SBI Clerk, PO, SO, and IBPS Exams and take up a big part of it. The Progression in a geometric series increases quickly, and that’s why the name is given such.
What is the formula to find the sum of a Geometric Progression?
Now, let us find how to write the formula of the sum of a geometric progression.
The sum of a geometric progression can be found up to n number of terms. In the formula below, the 1st term is a, and the common is termed as r.
Therefore, the formula is:
Sn=a.(rn-1)/(r-1)……………….., this is used when r is not equal to 1
Sn=an, this is used when r is equal to 1
Sn=a/(1-r), this is used to find the sum of an infinite number of terms when -1 < r < 1
If you need the sum up to infinite terms, then the formula is = a/(1-r).
The geometric series is formed when each member of the whole pattern of sequence is formed by multiplying it with the same number.
One needs to memories these very simple formulas to get well-versed with the chapter of Geometric Progression. There are only three formulas, so learning and understanding the chapters are not very difficult if practiced well.
Before closing the chapter, let us solve a very simple question!
The series of the GP is 3,6, 12,…. You need to find the first five terms. Your options are:
- (A) 18
- (B) 27
- (C) 1881
- (D) 93/4
If your answer to option C, then congrats, you have understood Geometric Progression.
If you don’t worry, in this geometric Progression, we have our n, which is 5, a is three, and our r is 2.
Note the terms:
Use the terms in the formula accordingly. We hope you did find your answer now. With a little practice, geometric progression becomes a very easy chapter.