Tables show common formulas helpful when you performing sequences related tasks such as sum of first n elements of arithmetic sequence or calculation arbitral element of geometric sequence.

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Some facts#

Numerical sequence (sometimes also called numerical progression) is a function whose arguments are natural numbers (1, 2, 3, etc.):

$\begin{alignedat}{4} f(1) & = a_1 & = & \text{ the first term of the sequence},\\ f(2) & = a_2 & = & \text{ the second term of the sequence},\\ f(3) & = a_3 & = & \text{ the third term of the sequence},\\ ...\\ f(n-1) & = a_{n-1} & = & \text{ the (n-1)-th term of the sequence},\\ f(n) & = a_{n} & = & \text{ the n-th term of the sequence},\\ f(n+1) & = a_{n+1} & = & \text{ the (n+1)-th term of the sequence},\\ \text{etc.} \end{alignedat}$
The sequence differs from the set in that its elements are ordered (the order of the elements matter).
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.

If you want to learn more about the arithmetic sequence, check our other calculator: Arithmetic sequence.
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.

If you want to learn more about the geometric sequence, check our other calculator: Geometric sequence.
In addition to the numerical sequence, we can consider sequences composed of other mathematical objects, e.g. functions. In this case, we would talk about function sequences.

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mathematical_tables_sequences · mathematical_tables_progressions · numerical_sequences_formulas · arithmetic_sequnces_formulas · geometric_sequences_formulas

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tablice_matematyczne_ciagi · wzory_na_ciagi_liczbowe · wzory_na_ciag_arytmetyczny · wzory_na_ciag_geometryczny

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