In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero 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.
Examples of a geometric sequence are powers r/^{/k} of a fixed non-zero number r, such as 2k (a) and 3k. The general form of a geometric sequence is
\(a,ar,ar^{2},ar^{3},ar^{4},\ldots\)
where r ≠ 0 is the common ratio and a ≠ 0 is a scale factor, equal to the sequence’s start value.
The distinction between a progression and a series is that a progression is a sequence, whereas a series is a sum.
Geometric sequence
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“Geometric Progression.” 2022. Wikipedia, September. https://en.wikipedia.org/w/index.php?title=Geometric_progression&oldid=1112468108.