Find the nth term and view the full sequence
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.
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).
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.