A geomtric sequence is a sequence of numbers where the ratio between successive terms is a constant. Using $a$ for the first term and $r$ for the ratio, the sequence is then:

• $a,~ar,~ar^2,~ar^3,~ar^4,~\ldots$
Counting $a$ as term number 1, or the first term, we can see that

• term number 2 is $ar,$ or $ar^1,$
• term number 3 is $ar^2,$
• term number 4 is $ar^3,$
and so on. The exponent is always one less than number of the term. Thus the $n^{th}$ term is $ar^{n-1}.$

Compare with

CauchySequence (none) (none)
ArithmeticSequence
GeneralSequence
MathematicsTaxonomy

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