Geometric progression
In mathematics,geometric progression issequencenumbers such thatquotientany two successive members ofsequence isconstant. For instance,sequence 3, 6, 12, 24, 48, ... isgeometric progressioncommon quotient 2.Ifinitial term ofgeometric progressiona andcommon quotientsuccessive membersr, thenn-th term ofsequencegiven by a·rn, n = 0, 1, 2, ...
The sum ofnumbers ingeometric progressioncalledgeometric series. A convenient formulageometric seriesavailable.
See also arithmetic progression. Note thattwo kindsprogressionrelated: takinglogarithmeach term ingeometric progression yields an arithmetic one.
One ordinarily distinguishes between two kindsprogressions, arithmeticalgeometrical, corresponding toproportions called arithmeticalgeometrical. Butword 'proportion' seems rather inappropriate as appliedarithmetical proportion.
The ideaproportionalready well established by usageit corresponds solelywhatcalled geometrical proportion; when we say generally that one thingproportionalanother, we understand by proportion equalityratios only, asgeometrical proportion,never equalitydifferences asarithmetical proportion.
One cannot see whyproportion called arithmeticalany more arithmetical than that whichcalled geometrical, nor whylattermore geometrical thanformer. Oncontrary,primitive ideageometrical proportionbased on arithmetic, fornotionratios springs essentially fromconsiderationnumbers
