Number Sequence Calculator – Arithmetic, Geometric, Fibonacci & Series
This Number Sequence Calculator helps you explore arithmetic sequences, geometric sequences, Fibonacci-style patterns, and series sums. It also includes a basic pattern detector that can guess whether a list of numbers is arithmetic or geometric and suggest the next term.
Arithmetic Sequences
In an arithmetic sequence, the difference between consecutive terms is constant. If the first term is a₁ and the common difference is d, then:
The sum of the first n terms, Sₙ, is:
Geometric Sequences
In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio r. If the first term is a₁, then:
For r ≠ 1, the sum of the first n terms is:
Fibonacci-Style Sequences
Fibonacci-like sequences are defined by a recurrence relation of the form aₙ = aₙ₋₁ + aₙ₋₂ with two starting values. This calculator lets you generate Fibonacci, Lucas, and fully custom versions by choosing the first two terms and the length of the sequence.
Series Sums
The series tab focuses on the total sum of arithmetic or geometric sequences. Enter the first term, difference or ratio, and the number of terms to find Sₙ and the nᵗʰ term in one place.
Pattern Detection
The pattern detector analyzes your list of numbers to see if it matches a simple arithmetic or geometric pattern. If it finds a match, it reports the pattern and predicts the next term and the next k terms.
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