This arithmetic sequence calculator can help you find a specific number within an arithmetic progression and all the other figures if you specify the first number, common difference (step) and which number/order to obtain. You can learn more about the arithmetic series below the form.

## How does this arithmetic sequence calculator work?

An arithmetic progression which is also called an **arithmetic sequence** represents a sequence of numbers (sequence is defined as an ordered list of objects, in our case numbers - members) with the particularity that the difference between any two consecutive numbers is constant. For example, the sequence 3, 6, 9, 12, 15, 18, 21, 24… is an arithmetic progression having a common difference of 3.

The formulas applied by this arithmetic sequence calculator can be written as explained below while the following conventions are made:

- the initial term of the arithmetic progression is marked with a_{1};

- the step/common difference is marked with d;

- the nth term of the sequence is a_{n};

- the number of terms in the arithmetic progression is n;

- the sum of the finite arithmetic progression is by convention marked with S;

- the mean value of arithmetic series is x̅;

- standard deviation of any arithmetic progression is σ. Then:

a_{n }= a_{1 }+ d(n - 1)

S = [n(a_{1}+a_{n)}]/2

x̅ = (a_{1}+a_{n)}/2

σ = |d|*√((n-1)*(n+1)/12)

## Example of an arithmetic progression calculation

Assuming that a_{1 }= 5, d = 8 and that we want to find which is the 55^{th} number in our arithmetic sequence, the following figures will result:

■ The 55^{th} value of the sequence (a_{55}) is 437

■ Sample of the first ten numbers in the sequence: 5, 13, 21, 29, 37, 45, 53, 61, 69, 77

■ Sum of all numbers until the 55^{th}: 12155

■ The mean value of the series: 221

■ Standard deviation: 126.9961

10 Jun, 2015