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# 8 Examples of Geometric Sequences

September 28, 2023
written by Rida Mirza

In mathematics, Geometric sequences are formed by multiplying each term by a fixed, nonzero number called the common ratio. These sequences can be found in various aspects of our lives, showcasing the beauty of mathematical patterns.

## Examples of Geometric Sequences

These are eight examples of geometric series.

### 1: The Financial Geometric Sequence

One of the most important geometric sequences is in finance, especially in the context of compound interest. When you earn interest on an investment that compounds periodically, you are essentially witnessing a geometric sequence at work.

### 2: A Natural Geometric Sequence

In the natural world, bacteria serve as an example of geometric sequences through their rapid reproduction. Each generation multiplies by a fixed factor, resulting in exponential growth.

### 3: Harmonic Geometric Progression

Music enthusiasts will be delighted to learn that musical notes follow a geometric sequence when arranged in octaves. The frequency of each note is double that of the previous note, creating harmonious musical progressions.

### 4: Self-Similar Geometric Sequences

Fractals are complex geometric shapes that exhibit self-similarity at different scales. These intricate structures can be described using geometric sequences, revealing the mathematical beauty inherent in natural patterns.

### 5: Modeling with Geometric Sequences

Demographers and biologists often use geometric sequences to model population growth rates. This approach helps predict future population sizes and trends.

### 6: Fibonacci Sequence

The famous Fibonacci sequence, where each term is the sum of the two preceding terms, can also be considered a geometric sequence with a unique twist. As you progress along the sequence, the ratio of consecutive terms approaches the golden ratio.

### 7: Geometric Art

M.C. Escher, a renowned artist, employed geometric sequences to create mesmerizing tessellations. These intricate patterns demonstrate the fusion of mathematics and art, where geometric sequences play a significant role.

### 8: Symmetry in Geometric Sequences

Crystals exhibit stunning geometric symmetry, often represented by geometric sequences. This symmetry is essential in understanding the crystalline structure of various materials and has implications in material science.

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