# Beta version

BETA TEST VERSION OF THIS ITEM

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

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

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

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

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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**:

$a_{n+1} = a_n \cdot r$where:

- $a_n$ - arbitrarily selected term,

- $a_{n+1}$ - the term just after $a_n$,

- $r$ - common ratio of geometric sequence.

- $a_n$ - arbitrarily selected term,
- The above formula should be understood as follows:
*if I know some element of the geometric sequence ($a_n$) and its common ratio ($d$), then I can calculate the next one ($a_{n + 1}$)*. - we can also define a geometric sequence in a slightly different way:

$a_{n} = a_{n-1} \cdot r$where:

- $a_n$ - arbitrarily selected term (except the first one: $n \neq 1$),

- $a_{n-1}$ - the term just before $a_n$,

- $r$ - the common ratio of geometric sequence.

- $a_n$ - arbitrarily selected term (except the first one: $n \neq 1$),
- Above alternative formula should be understood as follows:
*if I want to calculate some selected element of the geometric sequence ($a_{n}$), then I need to know the previous one ($a_{n-1})$) and the common ration ($r$)*. - It is worth noting that the second formula
**does not work for the first element**($a_1$). 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 $a_1$,

- and the ratio of two consecutive terms $r$, so called
**common ratio of geometric sequence**:

$r = \frac{a_{n+1}}{a_n}$

- the first term $a_1$,
- 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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