Number Sequence Calculator
Generate arithmetic, geometric or Fibonacci sequences. Find the nth term, sum or list of any sequence given its starting parameters.
How to use the Number Sequence Calculator
- Enter your inputs into the Number Sequence Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The sequence formulas
Arithmetic nth: aₙ = a₁ + (n−1)·d · · · Geometric nth: aₙ = a₁·r^(n−1) · · · Fibonacci: Fₙ = Fₙ₋₁ + Fₙ₋₂
Arithmetic adds a constant difference d each term. Geometric multiplies by a constant ratio r. Fibonacci sums the two prior terms (after initial 0, 1 or 1, 1).
Worked example
Arithmetic with a₁=3, d=4: 3, 7, 11, 15, 19, 23... 10th term: 3 + 9×4 = 39. Geometric with a₁=2, r=3: 2, 6, 18, 54, 162... 6th term: 2 × 3⁵ = 486. Fibonacci: 0, 1, 1, 2, 3, 5, 8, 13, 21...
Frequently asked questions
How do I find the sum of a sequence?
Arithmetic: S = n(a₁ + aₙ)/2. Geometric (r ≠ 1): S = a₁(1 − rⁿ)/(1 − r). For infinite geometric with |r|<1: S = a₁/(1 − r).
What is the golden ratio in Fibonacci?
The ratio of consecutive Fibonacci numbers approaches the golden ratio φ ≈ 1.618 as n grows. This appears throughout nature, art and architecture.
Can the calculator handle other sequences?
Custom recursive sequences (like polynomial or factorial-based) can usually be expressed in terms of the supported types or computed in a spreadsheet.