In a geometric sequence, the ratio between each pair of consecutive terms is the same.
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In a geometric sequence, the ratio between each pair of consecutive terms is the same. This ratio is called the common ratio. Therefore, the next term can always be found by multiplying the previous term by the common ratio r.
Consequently, any pattern — either increasing or decreasing — that has a common ratio can be described using a geometric sequence. For example, as seen in Exploration 2, a sheet of paper is 0.1 mm thick, and the thickness doubles every time we fold it. Therefore, its thickness can be described by a geometric sequence.
The table above shows the thickness corresponding to each number of folds. If we think about the number of folds as the term number and the thickness as the term itself, we can see that this situation is described by the geometric sequence shown below.
0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, ...
In the same way, we can use geometric sequences to describe any pattern that increases or decreases by a constant factor.
