Number Sequence Calculator

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

Arithmetic Sequence Calculator

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

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

Geometric Sequence Calculator

definition: f_n = f_n-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; f_n=f_n-1+f_n-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:

f_n = f_n-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 + f_n)/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:

f_n = f_n-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
f_n = f_n-1 + f_n-2

the numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...