Number Sequence Calculator

There are many different types of number sequences. The following are calculators for some of them.

Arithmetic Sequence Calculator

definition: fn = fn-1 + f
example: 1, 3, 5, 7, 9 11, 13, ...

the first number
common difference (f)
the number to obtain
 

Geometric Sequence Calculator

definition: fn = fn-1 * r
example: 1, 2, 4, 8, 16, 32, 64, 128, ...

the first number
common ratio (r)
the number to obtain
 

Fibonacci Sequence Calculator

definition: f0=0; f1=1; fn=fn-1+fn-2;
example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

the number to obtain
 


Reference

By definition, a sequence is an ordered list of objects. Accordingly, a number sequence is an ordered list of numbers. Many different types of number sequences have been invented. We have calculators for the following three most common number sequences:

Arithmetic Sequence

An arithmetic sequence is a number sequence that the difference of any two successive numbers is a constant. The following is the formula:

    fn = fn-1 + f
      or
    a, a + f, a + 2f, a + 3f, a + 4f, ...
example:
    1, 3, 5, 7, 9 11, 13, ...
The sum of an arithmetic sequence with n members:
    n(f1 + fn)/2
      or
    an + n(n-1)/2

Geometric Sequence

A geometric sequence is a number sequence that each number after the first is the multiplication of the previous one with a fixed non-zero number. The following is the formula:

    fn = fn-1 * r
      or
    a, ar, ar2, ar3, ar4, ...
where:
    a is a scale factor
    r is the common ratio
example:
    1, 2, 4, 8, 16, 32, 64, 128, ...
The sum of a geometric sequence with n members:
    a(1-rn+1)/(1-r)
The product of a geometric sequence with n members:
    anr(n(n-1)/2)

Fibonacci Sequence

The Fibonacci sequence is a number sequence that the first two numbers are 0 and 1, and each subsequent number is the sum of the previous two. The following is the formula:
    f0 = 0
    f1 = 1
    fn = fn-1 + fn-2
the numbers:
    0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...