What is a Number Sequence Calculator?

A Number Sequence Calculator is an online tool that calculates or produces the terms of a mathematical sequence fast and precisely for free. It is used in finding the nᵗʰ term of a sequence and the sum of the first n terms of a sequence, as well as calculating each term, manually.

It handles typical mathematical schemes including arithmetic sequences (adding a constant amount of differences), geometric sequences (multiplying by a common ratio), and even exceptional sequences including the Fibonacci sequence or primes. If you happen to be a pupil completing homework or a professional performing data or algorithmic models, it gives you instant, exact results.

How Does the Number Sequence Calculator Work?

1. Select the sequence type: Arithmetic, Geometric, Fibonacci, or Prime.
2. Please enter the inputs:
   • First term (a₁)
   • Common difference (d) for arithmetic
   • Common ratio (r) for geometric
   • Number of terms (n)
3. Click Calculate — you’ll see the terms that were generated, the nᵗʰ term (aₙ), and partial sum (Sₙ) if it was applicable.
4. Copy or export the results for reports, assignments, or further analysis.

Formulas Used

Arithmetic Sequence

• nᵗʰ term: aₙ = a₁ + (n − 1)d
• Sum of first n terms: Sₙ = n/2 · (2a₁ + (n − 1)d)

Geometric Sequence

• nᵗʰ term: aₙ = a₁ × r⁽ⁿ⁻¹⁾
• Sum of first n terms (r ≠ 1): Sₙ = a₁ × (1 − rⁿ) / (1 − r)

Why Use This Calculator?

• Instant and precise sequence production
• Calculates nth terms and partial sums
• Supports arithmetic, geometric, Fibonacci, and prime sequences
• Easy to use on the move, tablet, or computer
• Ideal for education, research, and algorithm verification

Disclaimer

This Number Sequence Calculator is provided for educational and informational purposes only. Results are based on standard mathematical formulas and may include rounding. Always verify critical or professional calculations with authoritative mathematical references.