Sequences

These tools find the terms and sums of a sequence. They cover the general term and partial sums of arithmetic and geometric sequences (including whether the series converges or diverges), the nth Fibonacci number with a graph of its convergence to the golden ratio, and figurate numbers such as triangular, square, pentagonal, and hexagonal numbers.

Arithmetic Sequence Calculator (aₙ = a₁ + (n−1)d)

Enter the first term a₁ and common difference d to compute the nth term and partial sums of an arithmetic sequence. Includes a term table and bar chart.

Geometric Sequence Calculator (aₙ = a₁·rⁿ⁻¹)

Enter the first term a₁ and common ratio r to compute the nth term, partial sums, and infinite sum (when |r| < 1). Includes a term table and bar chart.

Fibonacci Sequence Calculator — Instant Nth Term & Golden Ratio Chart

Instantly compute any term of the Fibonacci sequence, exact up to F(100) using BigInt. See the ratio of consecutive terms converge to the golden ratio φ, explore Lucas numbers, and view a bar chart of the first N terms.

Figurate Numbers Calculator (Triangular, Square, Pentagonal, Hexagonal)

Calculate triangular, square, pentagonal, and hexagonal numbers from the 1st to the Nth term and compare them on a graph. Instantly compute the value of any nth term. Includes a reference table for terms 1-15.