Number Sequence Calculator

Find the nth term and view the full sequence

Fibonacci sequence: F₀ = 0, F₁ = 1, Fₙ = Fₙ₋₁ + Fₙ₋₂

10th Term

About the Number Sequence Calculator

This number sequence calculator computes the nth term and displays the full sequence for arithmetic (linear), geometric (exponential), and Fibonacci sequences. Understanding sequences is fundamental to algebra, calculus, and number theory.

The Formulas

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 arithmetic and geometric sequences?

An arithmetic sequence has a constant difference between consecutive terms (linear growth), while a geometric sequence has a constant ratio between consecutive terms (exponential growth or decay). For example, 2, 4, 6, 8 is arithmetic (d=2), but 2, 4, 8, 16 is geometric (r=2).

Where is the Fibonacci sequence found in nature?

The Fibonacci sequence appears in the spiral arrangement of sunflower seeds, pinecones, nautilus shells, leaf arrangements, and branching patterns in trees. The ratio of consecutive Fibonacci numbers approaches the golden ratio (φ ≈ 1.618), which is found throughout art and architecture.