Toolstia / Sequence calculator
Sequence calculator
Work out the nth term and the sum of the first n terms of an arithmetic or geometric sequence, see the first terms, and find the infinite sum of a geometric sequence when it exists. A Fibonacci mode gives exact numbers up to the 20,000th.
How it works
- Choose arithmetic, geometric or Fibonacci.
- Enter the first term, the common difference or ratio, and n.
- Read the term, the sum and the first terms.
Arithmetic
Each term adds a constant d. The nth term is a₁ + (n − 1)d and the sum is n(a₁ + aₙ) ÷ 2.
Geometric
Each term multiplies by a constant r. The nth term is a₁rⁿ⁻¹ and the sum is a₁(1 − rⁿ) ÷ (1 − r). When |r| is below 1 the sum to infinity is a₁ ÷ (1 − r).
Fibonacci
Each number is the sum of the two before it, starting 0, 1, 1, 2, 3, 5. Big-integer arithmetic gives every digit exactly.
Limits
n can be up to 100,000 for arithmetic and geometric sequences and up to 20,000 for Fibonacci.
Questions
Does Fibonacci start at 0 or 1?
This tool uses F₀ = 0 and F₁ = 1.
When does the infinite sum exist?
Only when the ratio is between −1 and 1.
Is anything uploaded?
No. Your input stays in your browser and is never sent anywhere.