# Geometric progression calculator

Geometric progression, often abbreviated as GP, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. This mathematical concept plays a crucial role in various fields and applications.

## Structure of Geometric Progression

In a geometric progression, each term is calculated using the formula:

\[a_n = a_1 \cdot r^{(n-1)}\]

Where:

- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(r\) is the common ratio, and
- \(n\) is the number of terms.

The general form of a geometric progression looks like this:

\[a_1, a_1 \cdot r, a_1 \cdot r^2, a_1 \cdot r^3, \ldots\]

## Key Properties of Geometric Progression

1. **Common Ratio (\(r\)):** The ratio between any two consecutive terms in a geometric progression is constant.

2. **Exponential Growth or Decay:** Depending on whether the common ratio is greater than 1 or between 0 and 1, a geometric progression exhibits exponential growth or decay, respectively.

## Applications of Geometric Progression

Geometric progressions find applications in various areas:

**Finance:**Compound interest calculations often involve geometric progressions.**Physics:**Concepts like exponential decay and growth are modeled using geometric progressions.**Biology:**Population growth and decay can be represented using geometric progressions.**Computer Science:**Algorithms and data structures may utilize geometric progressions.

Understanding geometric progression is essential for solving real-world problems and making informed decisions in diverse fields.

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