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geometric progression

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geometric progression

In mathematics, a sequence of terms (progression) in which each term is a constant multiple (called the common ratio) of the one preceding it. For example, 3, 12, 48, 192, 768, ... is a geometric progression with a common ratio 4, since each term is equal to the previous term multiplied by 4. Compare arithmetic progression.

The sum of n terms of a geometric series

1 + r + r2 + r3 + ... + rn − 1

is given by the formula

Sn = (1 − rn)/(1 − r) for all r ≠ 1.

For mod r < 1 (see absolute value), the geometric series can be summed to infinity:

S = 1/(1 − r).

In nature, many single-celled organisms reproduce by splitting in two so that one cell gives rise to 2, then 4, then 8 cells, and so on, forming a geometric sequence 1, 2, 4, 8, 16, 32, ..., in which the common ratio is 2.



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? Mentioned in ? References in periodicals archive
 
Since the base is square, each new layer shows a geometric progression, such as 1X1, 2X2, 3X3, and 4X4.
The geometric progression in terms of the types of different stories he can tell is endless.
This situation is similar to the development of SCSI, where the transition has gone from five megabytes per second to 160MB/sec utilizing a geometric progression.
 
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