This Geometric Sequence Calculator calculates the n-th term and the sum of the first n terms of a geometric sequence, given the first term of the sequence and the common ratio.
Geometric sequence formula
In mathematics, a geometric sequence, or geometric progression is a sequence of numbers where each term after the first can be obtained by multiplying the previous one by a fixed, non-zero number called the common ratio. So, the formula for the \(n\)-th term is:
$${ a }_{ n } ={ a }_{ 1 }{ r }^{ n-1 },$$
where \(r\) is the common ratio.
The sum of the numbers in a geometric progression, also known as a geometric series, is expressed by the following formula:
$${ a }_{ 1 }\frac { 1-{ r }^{ n } }{ 1-r }.$$
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