Number Sequence Generator
This number sequence generator builds arithmetic, geometric, Fibonacci, and custom sequences instantly and shows the nth term and the sum of all terms as you type. Pick a sequence type, enter your parameters, and the full list of numbers appears in real time.
Switch between four tabs to model a constant difference, a constant ratio, a Fibonacci-style sum, or your own formula using n. Built-in presets cover primes, factorials, squares, cubes, triangular numbers, and powers of 2 — useful for students checking homework, teachers preparing examples, and programmers exploring number patterns.
How to Use the Sequence Generator
Choose a sequence type
Click one of the four tabs: Arithmetic for a constant difference, Geometric for a constant ratio, Fibonacci for sum-based growth, or Custom for presets and your own formula.
Enter the parameters
Set the inputs for that type — for example first term, common difference, and number of terms for arithmetic; first term, common ratio, and number of terms for geometric; or two starting values for Fibonacci.
Read the results
The full sequence, the nth term, and the sum update instantly as you type. Fibonacci sequences also show the approximate golden ratio.
Copy the sequence
Click the copy button next to the sequence to copy every term to your clipboard as a comma-separated list, ready to paste anywhere.
Features
Arithmetic Sequence Calculator
Generate terms with a constant difference using aₙ = a₁ + (n − 1)d, and get the sum from Sₙ = n/2 × (2a₁ + (n − 1)d). Supports up to 1000 terms.
Geometric Sequence Calculator
Build terms with a constant ratio using aₙ = a₁ × r^(n − 1), with the series sum from Sₙ = a₁(1 − rⁿ)/(1 − r). Ideal for compound growth and decay.
Fibonacci Sequence Generator
Each number is the sum of the two before it. Set your own two starting values and see the approximate golden ratio (φ ≈ 1.618) from the last two terms.
Custom Sequence Builder
Write your own formula with n, or pick a preset: natural, even, odd, square, cube, triangular numbers, powers of 2, prime numbers, and factorials.
Real-Time Calculations
Results refresh the moment you change any input — there is no calculate button to press, just type and read the answer.
Comprehensive Results
For every sequence you get the complete list of terms, the nth term value, and the total sum — plus a one-click copy to grab the whole list.
Frequently Asked Questions
What's the difference between an arithmetic and a geometric sequence?
In an arithmetic sequence you add a constant value, the common difference, to move to the next term. In a geometric sequence you multiply by a constant value, the common ratio. Use the Arithmetic tab for the first and the Geometric tab for the second.
How do I find the nth term of an arithmetic sequence?
The nth term is aₙ = a₁ + (n − 1)d, where a₁ is the first term, d is the common difference, and n is the position. Enter those values on the Arithmetic tab and the nth term is shown automatically as the last number in the list.
What is the formula for the sum of a geometric sequence?
The sum of the first n terms is Sₙ = a₁(1 − rⁿ)/(1 − r) when the common ratio r is not 1. The Geometric tab applies this formula for you and displays the sum next to the sequence.
What is the golden ratio in a Fibonacci sequence?
The golden ratio (φ ≈ 1.618) is the ratio between consecutive Fibonacci numbers as the sequence grows. This tool approximates it by dividing the last term by the second-to-last term in your sequence.
How do I create a custom formula?
On the Custom tab, type a math expression that uses n as the term position — for example n*n for squares, 2*n-1 for odd numbers, or 2**n for powers of 2. You can also pick a ready-made preset from the dropdown.
What operators and functions can I use in a custom formula?
You can use +, -, *, /, % (modulo), and ** or ^ for powers. Math functions such as Math.sqrt(), Math.pow(), and Math.abs() are also available.
What is the maximum number of terms I can generate?
Arithmetic sequences support up to 1000 terms. Geometric, Fibonacci, and Custom sequences are capped at 100 terms to keep the numbers manageable and avoid extremely large values.
Can I use decimal numbers?
Yes. Arithmetic and geometric sequences accept decimal inputs for the first term, difference, or ratio. Fibonacci works best with whole numbers since each term is built by addition.
No comments yet. Be the first to comment!