In mathematics, a geometric progression, also known as 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. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2. The sum of the terms of a geometric progression, or of an initial segment of a geometric progression, is known as a geometric series.
Thus, the general form of a geometric sequence is
and that of a geometric series is
where r ≠ 0 is the common ratio and a is a scale factor, equal to the sequence's start value.
Read more about Geometric Progression: Elementary Properties, Geometric Series, Product, Relationship To Geometry and Euclid's Work
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