A geometric sequence 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 type of sequence is characterized by exponential growth or decay, depending on whether the common ratio is greater than or less than one.

Geometric Sequence

geometric sequence

sequence of numbers

Fixed non-zero number

The common ratio is a constant factor between consecutive terms of a geometric sequence, determining the sequence's multiplicative progression. It is essential for identifying patterns, predicting future terms, and solving problems related to exponential growth or decay.

common ratio

Exponential growth describes a process where the rate of increase is proportional to the current value, leading to the quantity growing at an increasingly rapid rate. This type of growth is characterized by a constant doubling time and is often observed in populations, investments, and certain natural phenomena.

exponential growth

Exponential decay describes a process where a quantity decreases at a rate proportional to its current value, leading to a rapid decline that slows over time. This mathematical model is crucial for understanding phenomena such as radioactive decay, population decline, and depreciation of assets.

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