# Real-life Applications of Geometric Progression

Last Updated : 04 Apr, 2024

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.

## 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:

### 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

Some of the common real life application of geometric progression are:

• Finance: Compound Interest
• Medicine: Bacteria Culters

## Finance

Concept of geometric progression is a cornerstone in finance, used widely for forecasting and planning financial growth and strategies. Financial analysts leverage geometric progressions extensively to decipher potential growth trends for investments and generate substantial financial forecasts.

For example, imagine you invest â‚¹1,000 into a savings account compounding interest annually at a rate of 5%. Initially, your balance is â‚¹1,000. After a year, the balance isn’t just â‚¹1,000 plus 5% of â‚¹1,000; instead, the interest is calculated on the balance of â‚¹1,000 plus the interest already accrued, i.e., (â‚¹1,000 + â‚¹50).

Therefore, after one year, your deposit has risen to â‚¹1,000 Ã— 1.05 = â‚¹1,050.

In the second year, you’re earning interest not just on your initial principal amount of â‚¹1,000, but also on the â‚¹50 interest accumulated in the first year. So, at the end of the second year, the amount in the account would be â‚¹1,050 Ã— 1.05 = â‚¹1,102.50

## Medicine

In pharmacokinetic which is the study of how a drug is absorbed, distributed, metabolized, and excreted by the body, geometric progression is also very fundamental. From the above example, assuming the medication has a half-life of 4 hours, for the first dose of 400mg, half of the amount of the drug, i.e. 200mg would remain in the body after 4 hours.

The 600mg after 4 hours when a second dose of 400mg drug will be absorbed in a graph of t vs A, and after another 4 hours, now totaling 8 hours which is distinct is another half-life. Therefore 300mg remained in the body after 8 hours. The 700mg that remains in the body was the sum of the two doses.

This pattern continues, forming a geometric progression (400, 600, 700…) . This provides a model for doctors to determine appropriate dosage levels and frequencies, ensuring a consistent and effective concentration of medication in the patient’s bloodstream

## Conclusion

Geometric progression is not just a mathematical theory, it has various applicaitons in real life. From the exponential growth of money in banks, rapid propagation of bacteria, decay of radioactive substances to the progression of technological advancements. Understanding geometric progressions enables us to comprehend the world more completely and make informed predictions about the future.

## FAQs: Geometric Progression

### Define geometric progression.

Geometric progression is a sequence of numbers where any term after the first can be found by multiplying the preceding term by a constant number, known as the common ratio.

### How does geometric progression apply to finance?

In finance, geometric progressions are used to calculate compound interest, which utilises the concept of geometric series to determine the growth of investments over a certain period of time.

### How can geometric progressions represent exponential growth?

Geometric progressions utilise a common ratio that amplifies each step in the sequence, which can effectively represent exponential growth or doubling patterns found in various real-world contexts like population growth, information technology advancements, and bacterial proliferation.

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