Number Sequence Calculator
Calculate arithmetic and geometric sequence terms, nth term, sum of n terms, and common difference or ratio. Find any term in any sequence. Free.
Number Sequence Calculator
toolznova.com • Free Calculator
How to Use
Calculate sequences in 3 steps.
Choose Sequence Type
Select arithmetic (adding) or geometric (multiplying) sequence.
Enter Parameters
Enter first term, common difference/ratio, and desired term number.
Get Results
Click Calculate for nth term, sum, formula, and first terms list.
Why ToolzNova?
Instant
Results in milliseconds.
Accurate
Precise formulas every time.
Private
No data sent anywhere.
Everywhere
Mobile, tablet, desktop.
Why Calculate Sequences?
- Mathematics: Sequences are fundamental to algebra and calculus.
- Finance: Simple interest is arithmetic, compound interest is geometric.
- Physics: Uniformly accelerated motion follows arithmetic sequence.
- Computer Science: Algorithm analysis uses sequence convergence.
- Nature: Fibonacci sequence appears throughout natural patterns.
- Patterns: Identify and extend numerical patterns in data.
Tips & Examples
- Arithmetic: each term adds constant d. Example: 2,5,8,11,14 (d=3).
- Geometric: each term multiplies by constant r. Example: 2,6,18,54 (r=3).
- Arithmetic nth term: a + (n-1)d.
- Geometric nth term: a × r^(n-1).
- Sum of arithmetic series: n/2 × (first + last term).
- Geometric series with |r|<1 converges to a/(1-r) as n→∞.
Free Number Sequence Calculator Online
ToolzNova's free number sequence calculator finds the nth term and sum of arithmetic and geometric sequences. Shows the formula used and first 8 terms of the sequence.
Arithmetic sequences have a constant difference between terms. Geometric sequences have a constant ratio. Both are fundamental in mathematics, physics, and financial calculations.
Sequence Formulas
Arithmetic nth term: aₙ = a+(n-1)d. Sum: Sₙ = n/2(2a+(n-1)d). Geometric nth term: aₙ = a×r^(n-1). Sum: Sₙ = a(1-rⁿ)/(1-r) for r≠1.