Number Sequence Calculator
Identify and continue arithmetic or geometric number sequences.
Arithmetic Sequence Calculator
definition: an = a₁ + f × (n-1)
example: 1, 3, 5, 7, 9, 11, 13, ...
Geometric Sequence Calculator
definition: an = a × rn-1
example: 1, 2, 4, 8, 16, 32, 64, 128, ...
Fibonacci Sequence Calculator
definition: a₀=0; a₁=1; an = an-1 + an-2
example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
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Calculate Terms in Arithmetic, Geometric, and Fibonacci Sequences
Our Number Sequence Calculator helps you find any term in an arithmetic, geometric, or Fibonacci sequence based on the series' rules.
What is a Number Sequence Calculator?
A Number Sequence Calculator is a tool that finds a specific term in a mathematical sequence based on a defined rule. This calculator supports three of the most common types: arithmetic sequences (where a constant number is added), geometric sequences (where a constant number is multiplied), and the Fibonacci sequence (where each term is the sum of the two preceding ones).
How It Works: The Formulas
The calculator applies the standard formula for each sequence type:
Arithmetic: aₙ = a₁ + (n-1)d
Geometric: aₙ = a₁ × rⁿ⁻¹
Fibonacci: Fₙ = Fₙ₋₁ + Fₙ₋₂
Frequently Asked Questions
What is the difference between an arithmetic and a geometric sequence?
In an arithmetic sequence, the difference between consecutive terms is constant (e.g., 2, 5, 8, 11... where the difference is 3). In a geometric sequence, the ratio between consecutive terms is constant (e.g., 2, 6, 18, 54... where the ratio is 3).
How do you find the nth term of an arithmetic sequence?
The formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n-1)d, where a₁ is the first term, n is the term number, and d is the common difference.
What is the Fibonacci sequence?
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. The sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.
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