Arithmetic Sequence Calculator

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 a₁;

- 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 = a₁ + d(n - 1)

S = [n(a₁+a_n)]/2

x̅ = (a₁+a_n)/2

σ = |d|*√((n-1)*(n+1)/12)

Example of an arithmetic progression calculation

Assuming that a₁ = 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 (a₅₅) 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