# 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
**arithmetic sequence**is the sequence in which each successive element**differs from the previous one by a fixed value d**:

$a_{n+1} = a_n + d$where:

- $a_n$ - arbitrarily selected term,

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

- $d$ - common difference of arithmetic sequence.

- $a_n$ - arbitrarily selected term,
- The above formula should be understood as follows:
*if I know some element of the arithmetic sequence ($a_n$) and its difference ($r$), then I can calculate the next one ($a_{n + 1}$)*. - The above formula can be also formulated as below:

$a_{n} = a_{n-1} + d$where:

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

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

- $d$ - the common difference of arithmetic 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 arithmetic sequence ($a_{n}$), then I need to know the previous one ($a_{n-1})$) and the common difference ($d$)*. - 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 arithmetic sequence, it is enough to know two values:

- the first term $a_1$,

- and the difference between two consecutive terms $d$, so called
**common difference of arithmetic sequence**:

$d = a_{n+1} - a_n$

- the first term $a_1$,
- Arithmetic sequence is sometimes called an
**arithmetic progression**. - If you are interested in the properties of sequences, then you can check out our other calculators:

# Tags and links to this website

Tags:

arithmetic_sequence · arithmetic_progression · sum_of_arithmetic_sequence · common_difference_of_arithmetic_sequence · nth_term_of_arithmetic_progression

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