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A geometric series is a series associated with a geometric sequence, i.e., the ratio (or quotient) q of two consecutive terms is the same for each pair.

Thus, every geometric series has the form

$a+aq+aq^{2}+aq^{3}+\cdots$

where the quotient (ratio) of the (n+1)th and the nth term is

${\frac {aq^{n}}{aq^{n-1}}}=q.$

The sum of the first n terms of a geometric sequence is called the n-th partial sum (of the series); its formula is given below (S_n).

An infinite geometric series (i.e., a series with an infinite number of terms) converges if and only if |q|<1, in which case its sum is $a \over 1-q$, where a is the first term of the series.

In finance, since compound interest generates a geometric sequence, regular payments together with compound interest lead to a geometric series.

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