Number Sequence Calculator
Identify sequence types, calculate terms, sum of sequences, explicit formulas, and recursive relations for Arithmetic, Geometric, Fibonacci, and custom sequences.
Calculate Sequence from Explicit Formula
Specify a formula in terms of n (e.g., 2*n + 1, n^2 - 3, 3 * 2^(n-1)) to calculate terms and sum.
Identify Sequence & Calculate Terms
Enter a comma-separated sequence of numbers (e.g., 2, 5, 8, 11, 14 or 3, 6, 12, 24) to auto-detect the rule, formula, common difference/ratio, next terms, and sum.
How To Use the Number Sequence Calculator
A number sequence is an ordered list of numbers that follow a specific pattern or rule.
- Arithmetic Sequence: The difference between consecutive terms is constant (Common Difference d).
- Geometric Sequence: The ratio between consecutive terms is constant (Common Ratio r).
- Fibonacci Sequence: Each term is the sum of the preceding two terms (Fn = Fn-1 + Fn-2).
Frequently Asked Questions (FAQs)
An explicit formula designates the n-th term an directly as a function of n, allowing you to calculate any term in the sequence without finding the previous terms.
In an Arithmetic sequence, subtract any term from the following term (d = a2 - a1). In a Geometric sequence, divide any term by the preceding term (r = a2 / a1).
Our calculator checks for Polynomial/Quadratic patterns (constant 2nd differences), Fibonacci patterns, and custom explicit algebraic functions.