Number Sequence Calculator | Math Sequence Generator
Generate arithmetic, geometric, and Fibonacci sequences with our free online calculator. Perfect for mathematics education, pattern recognition, and sequence analysis.
Category: Math
Number Sequence Calculator
Generate arithmetic, geometric, and Fibonacci sequences.
Formula:
a, a+d, a+2d, a+3d, ...
an = a + (n-1)d
Frequently Asked Questions
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers where each term differs from the previous one by a constant value, called the common difference. For example, 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3.
How do you calculate a geometric sequence?
A geometric sequence is a sequence where each term is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, 2, 6, 18, 54, ... is a geometric sequence with a common ratio of 3. The formula for the nth term is a₁ × r^(n-1), where a₁ is the first term and r is the common ratio.
What makes the Fibonacci sequence special?
The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, ...) is special because each number is the sum of the two preceding ones. It appears frequently in nature, art, and mathematics. The ratio of consecutive Fibonacci numbers approaches the golden ratio (approximately 1.618), which is found in many natural phenomena and is aesthetically pleasing.
How can I find the sum of a number sequence?
For an arithmetic sequence, the sum of n terms can be found using the formula: Sum = n/2 × (first term + last term). For a geometric sequence with first term a and common ratio r (where r ≠ 1), the sum of n terms is: Sum = a × (1 - r^n) / (1 - r). For the Fibonacci sequence, there isn't a simple formula, but our calculator computes the sum automatically.