About this tool
Work with arithmetic and geometric sequences in one place. Choose Arithmetic or Geometric and enter the first term with the common difference or ratio and a term number, or pick Auto-detect and paste a comma-separated list to have the pattern found for you. Results include the nth term, the sum of the first n terms, and (for a converging geometric series) the sum to infinity, plus a preview of the first few terms. It all runs live in your browser.
For an arithmetic sequence the nth term is aₙ = a1 + (n-1)d and the sum is Sₙ = n/2 * (2a1 + (n-1)d). For a geometric sequence the nth term is aₙ = a1 * r^(n-1) and the sum is Sₙ = a1(1 - rⁿ)/(1 - r) when r ≠ 1; if |r| < 1 the infinite sum converges to S∞ = a1/(1 - r). Auto-detect checks a list for a constant difference between consecutive terms (arithmetic) or a constant ratio (geometric) and reports the common difference or ratio and the next term.
Use it to extend a pattern, total up a run of payments, or check homework. In Auto-detect mode enter at least three numbers so the pattern can be confirmed rather than guessed.