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.
Yes. The calculator can recognize common sequence patterns such as arithmetic, geometric, Fibonacci, and some polynomial sequences based on the values you enter.
Number sequences are widely used in mathematics, computer science, finance, engineering, statistics, and physics to identify patterns, model growth, and solve analytical problems.