Geometric progression calculator

A geometric progression is a sequence of numbers where the first term is non-zero, and each subsequent number is obtained by multiplying the previous one by the common ratio of the progression. An example of such a progression is 4, 8, 16, 32, 64, where the first term is 4, the common ratio is 2, and the number of terms is 5.

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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