QuantarizmQuantarizm
Calculators
Formula Library
Converters
Articles
QuantarizmQuantarizmMaking Numbers Meaningful.

Free math calculators, unit converters, and formula references — with clear steps.

Product

  • Calculators
  • Math
  • Financial
  • Formula Library
  • Converters
  • Articles

Company

  • About
  • Contact
Legal
  • Privacy Policy
  • Terms
  • Disclaimer
  • Cookies

© 2026 Quantarizm

Free tools · No account required

HomeCalculatorsConvertersFormula Library
  1. Home/
  2. Calculators/
  3. Math/
  4. Number Sequence Calculator

Number Sequence Calculator

Arithmetic, geometric, and Fibonacci sequences: nth term, partial sum, and term list with clear formulas.

Statistics

  • Average Calculator
  • Mean, Median, Mode, Range Calculator
  • Statistics Calculator
  • Standard Deviation Calculator
  • Number Sequence Calculator
  • Probability Calculator
  • Permutation and Combination Calculator
  • Sample Size Calculator
  • Z-score Calculator
  • Confidence Interval Calculator
  • P-value Calculator

How it works

Arithmetic: constant difference. Geometric: constant ratio. Fibonacci: each term is the sum of the previous two (F₀=0, F₁=1).

aₙ=a₁+d(n−1) · aₙ=a rⁿ⁻¹ · Fₙ=Fₙ₋₁+Fₙ₋₂

When to use

Use this tool when you need to: arithmetic odds: a₁=1, d=2, n=5 → a₅=9, S₅=25. Geometric powers of 2: a₈=128. Fibonacci F₁₀=55.

How to use this tool

  1. Enter your values in the fields above.
  2. Review the formula and any mode options for your problem.
  3. Read the result and the step-by-step solution.

Arithmetic odds: a₁=1, d=2, n=5 → a₅=9, S₅=25. Geometric powers of 2: a₈=128. Fibonacci F₁₀=55.

Frequently asked questions

What is the Number Sequence Calculator?
Arithmetic: constant difference. Geometric: constant ratio. Fibonacci: each term is the sum of the previous two (F₀=0, F₁=1).
How do I use the Number Sequence Calculator?
Enter the required values, then calculate. The Number Sequence Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Number Sequence Calculator use?
aₙ=a₁+d(n−1) · aₙ=a rⁿ⁻¹ · Fₙ=Fₙ₋₁+Fₙ₋₂

You may also like

  • Average CalculatorArithmetic and weighted mean with a visual sum÷count layout and step-by-step work.→
  • Mean, Median, Mode, Range CalculatorArithmetic mean, median, mode(s), and range for comma-separated data — with ordered list, frequency table, and worked steps.→
  • Statistics CalculatorArithmetic and geometric means, σ and s, variance, quartiles, IQR, and Σx / Σx² from a comma-separated list.→
  • Standard Deviation CalculatorPopulation σ and sample s with variance, mean, sum, standard error, and margin of error for the mean.→
  • Probability CalculatorIndependent two-event probabilities, solver, series of trials, normal range area, simple favorable/total, and Bayes.→
  • Permutation and Combination CalculatornPr and nCr without replacement, plus with-replacement n^r and multichoose, with factorials and steps.→

Browse categories

  • General
  • Geometry

Other categories

  • General
  • Geometry
All math calculators→

Popular

  • Percentage Calculator
  • Average Calculator
  • Fraction Calculator
  • Area Calculator
All math calculators→

Number sequence calculator

Find the nth term and partial sum of an arithmetic or geometric sequence, or a Fibonacci number Fₙ (with F₀ = 0, F₁ = 1).

Sequence type

aₙ = a₁ + d × (n − 1) · example: 1, 3, 5, 7, 9, …

n is 1-based: n = 1 is the first number. Sum Sₙ = n × (first + last) / 2.

Try an example

How it works

What is a number sequence?

A sequence is an ordered list of objects; a number sequence is an ordered list of numbers that follow a pattern. Each element is a term; the number of terms is the length (finite or infinite). Order matters, and the same values can appear more than once. Sequences are written by listing terms or by an indexed formula for the nth term — and series are what you get by summing sequence terms.

Arithmetic sequence

An arithmetic sequence has a constant difference d between successive terms: aₙ = a₁ + d×(n−1). Example: 1, 3, 5, 7, 9 with d = 2 gives a₅ = 1 + 2×4 = 9. The sum of the first n terms is Sₙ = n×(a₁ + aₙ)/2 — for that example S₅ = 5×(1+9)/2 = 25.

Geometric sequence

A geometric sequence multiplies by a fixed common ratio r each step: aₙ = a × rⁿ⁻¹. Example: 1, 2, 4, 8, … has a = 1, r = 2 so a₈ = 1×2⁷ = 128. The finite sum is Sₙ = a(1−rⁿ)/(1−r) when r ≠ 1 (e.g. through n = 3: 1+2+4 = 7).

Fibonacci sequence

Fibonacci: F₀ = 0, F₁ = 1, and every later term is the sum of the two before it (0, 1, 1, 2, 3, 5, 8, 13, …). These numbers show up in algorithms, economics, and nature. This tool also reports Σ Fᵢ from 0 through n using Fₙ₊₂ − 1.

Related calculators

Descriptive stats tools share the same data-entry style. Average focuses on the mean alone; sequences generate ordered lists instead of summarizing a sample.

  • Mean, Median, Mode, Range Calculator
  • Statistics Calculator
  • Standard Deviation Calculator
  • Sample Size Calculator
  • Probability Calculator
  • Average Calculator