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A geometric series is a series of numbers where each term is found by multiplying the previous term by a fixed, non-zero number called the common ratio (denoted by 'r'). In other words, a series is geometric if the ratio between any two consecutive terms is always the same. A geometric series can be represented as: a, ar, ar^2, ar^3, ..., ar^n, ...

The common ratio (r) is the factor by which we multiply each term to get the next term in the series. The ratio is a constant value and can be any non-zero number (positive, negative, or even a fraction). The common ratio can be found by dividing any term in the series by its preceding term. For example, in a geometric series, if T_{n} and T_{n-1} are two consecutive terms, then the common ratio (r) can be calculated as: r = \frac{T_{n}}{T_{n-1}}

The common ratio significantly affects the behavior and properties of a geometric series. Depending on the value of r, the series can behave differently: 1. If 0 < r < 1, the series converges, i.e., it has a finite sum. As n goes to infinity, the terms in the series get smaller and approach zero. The series is said to be a convergent geometric series. 2. If r > 1 or r < -1, the series diverges, i.e., it does not have a finite sum. As n goes to infinity, the terms in the series increase without bound. The series is said to be a divergent geometric series. 3. If -1 < r < 0, the series converges, but the terms alternate in sign. As n goes to infinity, the terms in the series get smaller and approach zero. The series is also a convergent geometric series. In summary, the ratio of a geometric series is the constant factor by which each term is multiplied to get the next term in the series. A series is geometric if the ratio between any two consecutive terms is always the same. The common ratio determines whether a geometric series converges or diverges and how its terms behave.