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Number Sequence Calculator
Work with arithmetic, geometric, and Fibonacci sequences. Find the nth term, list the first n terms, and compute the sum of the sequence.
Arithmetic Sequence Calculator
Definition: aโ = aโ + f ร (n โ 1)
Example: 1, 3, 5, 7, 9, 11, 13, โฆ
Geometric Sequence Calculator
Definition: aโ = a ร r^(n โ 1)
Example: 1, 2, 4, 8, 16, 32, 64, 128, โฆ
Fibonacci Sequence Calculator
Definition: aโ = 0; aโ = 1; aโ = aโโโ + aโโโ
Example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, โฆ
Number sequence calculator guide
A number sequence calculator evaluates ordered lists of numbers that follow a rule. The three patterns covered here are arithmetic, geometric, and Fibonacci sequences, which cover the most common cases used in schoolwork, interview prep, finance math, and algorithmic puzzles.
An arithmetic sequence adds a fixed amount, called the common difference, between consecutive terms. Starting at a first term aโ, the nth term is aโ plus (n โ 1) times the common difference. The series sum is simple because the terms grow linearly, which gives a handy closed form.
A geometric sequence multiplies by a fixed amount, called the common ratio, between consecutive terms. Starting at a first term a, the nth term is a times r raised to the power n โ 1. When the ratio is between โ1 and 1, the finite sum converges to a stable value.
A Fibonacci sequence is defined by two seed values and a recurrence where each term is the sum of the previous two. It is widely studied in mathematics and nature, and it also appears in programming interviews and dynamic programming tutorials.
Use this tool to explore each sequence, preview the first n terms, compute the sum of the first n terms, and read a clear step-by-step breakdown. Inputs accept decimals where appropriate, and outputs are formatted for easy scanning.
This page is designed as a quick practical reference. The educational material below expands on formulas, examples, and common pitfalls so learners can build a solid intuition for sequences and series.
How to use
- Pick the sequence type: arithmetic, geometric, or Fibonacci.
- Enter the first term and the common difference or ratio as needed.
- Enter n, the index of the term you want to find.
- Read the nth term, the sum of the first n terms, and the term list.
- Open Steps to see the formulas applied to your input.
Core formulas
Arithmetic: aโ = aโ + (n โ 1) f; Sโ = n ร (aโ + aโ) / 2. Geometric: aโ = a ร r^(n โ 1); if r โ 1, Sโ = a ร (1 โ rโฟ) / (1 โ r). Fibonacci: Fโ = 0, Fโ = 1, Fโ = Fโโโ + Fโโโ; sum of first n Fibonacci numbers equals Fโโโ โ 1.
Notes and limitations
- n must be a positive integer. For very large n, output is capped to avoid slowdowns.
- Geometric sequences with large |r| can produce very big or very small numbers.
- Fibonacci computations use arbitrary-precision arithmetic for exact large results.
- Decimal inputs are accepted for the arithmetic and geometric types.
FAQ
What is an arithmetic sequence?
A list where the difference between consecutive terms is constant, called the common difference.
What is a geometric sequence?
A list where the ratio between consecutive terms is constant, called the common ratio.
What is the Fibonacci sequence?
A sequence starting with 0 and 1 where every next term is the sum of the previous two.
Can I use negative or decimal inputs?
Yes. Arithmetic and geometric sequences accept signed decimal values for the first term, difference, or ratio.
Why do I see large numbers?
Geometric and Fibonacci sequences grow quickly. Large n produces long results that can exceed screen width.