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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 * Arithmetic sequence * General sequence