Geometric Progression

A series whereby each term is generated by multiplying the previous term by the common ratio (r)

u_n = ar^(n-1) (Where a is the first term u₁)

eg. 1,2,4,8,16,32 is a geometric progression with a common ratio of 2.

The common ratio can be obtained by taking any two consecutive terms and dividing the second by the first. (ie. u_(n+1) / (u_n) = r ) If the common ratio for any 2 pairs of terms is not the same then the series is not a geometric progression and the common ratio is meaningless/nonexistant. (After all, it is a common ratio... so how could anything work if it wasnt common to all the terms?)

Geometric growth is also frequently incorrectly dubbed exponential growth. Most of the time, when your first urge is to say "exponential growth", you really mean geometric.

Mathemetically, exponential growth is growth of the form

y^x

where x is not a constant. Most of the phenomena we observe and comment on are of the form

xⁿ

where n is a constant. When in doubt, say geometric.