Geometric Progression
Geometric progression (also known as a geometric sequence) is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
If the first term of the sequence is ‘a’ and the common ratio is ‘r’, then the nth term of the sequence is given by arn-1. General geometric progression can be written as:
a, ar, ar2, ar3, ar4, . . . , arn-1
Examples of Geometric Progression
Some examples of Geometric progression are listed below:
- 2, 4, 8, 16, 32 . . .
Common Ratio: 2
- 100, 50, 25, 12.5, 6.25 . . .
Common Ratio: 0.5
- 1/2, 1/4, 1/8, 1/16, 1/32 . . .
Common Ratio: 1/2
- -3, 6, -12, 24, -48 . . .
Common Ratio: -2
Real-life Applications of Geometric Progression
Geometric Progression is a sequence of numbers whereby each term following the first can be derived by multiplying the preceding term by a fixed, non-zero number called the common ratio. For example, the series 2, 4, 8, 16, 32 is a geometric progression with a common ratio of 2. It may appear to be a purely academic concept, but it is widely used in our day-to-day life. From calculating compound interest to estimating the number of bacteria in a culture, geometric progression is applied. We will discuss these applications of geometric progression in detail in this article.
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