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 a1;
- the step/common difference is marked with d;
- the nth term of the sequence is an;
- 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:
an = a1 + d(n - 1)
S = [n(a1+an)]/2
x̅ = (a1+an)/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 55th number in our arithmetic sequence, the following figures will result:
■ The 55th 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 55th: 12155
■ The mean value of the series: 221
■ Standard deviation: 126.996110 Jun, 2015