Geometric progression calculator
Calculator for tasks related to geometric sequences such as sum of n first elements or calculation of selected n-th term of the progression.

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This online calculator is currently under heavy development. It may or it may NOT work correctly.
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Some facts

  • The geometric sequence is a sequence in which each successive element is r times greater than the previous one:
    an+1=anra_{n+1} = a_n \cdot r
    where:
    • ana_n - arbitrarily selected term,
    • an+1a_{n+1} - the term just after ana_n,
    • rr - common ratio of geometric sequence.
  • The above formula should be understood as follows: if I know some element of the geometric sequence (ana_n) and its common ratio (dd), then I can calculate the next one (an+1a_{n + 1}).
  • we can also define a geometric sequence in a slightly different way:
    an=an1ra_{n} = a_{n-1} \cdot r
    where:
    • ana_n - arbitrarily selected term (except the first one: n1n \neq 1),
    • an1a_{n-1} - the term just before ana_n,
    • rr - the common ratio of geometric sequence.
  • Above alternative formula should be understood as follows: if I want to calculate some selected element of the geometric sequence (ana_{n}), then I need to know the previous one (an1)a_{n-1})) and the common ration (rr).
  • It is worth noting that the second formula does not work for the first element (a1a_1). This is because the first term as the only one does not have the previous element.
  • In order to uniquely define the geometric sequence, it is enough to know two values:
    • the first term a1a_1,
    • and the ratio of two consecutive terms rr, so called common ratio of geometric sequence:
      r=an+1anr = \frac{a_{n+1}}{a_n}
  • Geometric sequence is sometimes called a geometric progression.
  • If you are interested in the properties of sequences, then you can check out our other calculators:

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