Number Sequence Generator
Generate classic sequences and see how they grow. The Difference column shows the gap to the previous term and the Running Total column keeps the cumulative sum — integer inputs use big-integer maths.
Sequence Type:
First Term:
Difference / Ratio:
Term Count:
Decimals:
Separator:
Generated Number
Download CSV
| No. | Result | Difference | Running Total |
|---|
Introduction to the tool and how to use it
The sequence generator and analyzer lists classic sequences in one go while revealing their growth pattern; the difference and running-sum columns next to each term are the two most common lenses for analyzing a sequence.
Supported sequence types:
· Arithmetic — a(n) = first term + (n-1) × common difference; first term 1 and difference 2 give 1, 3, 5, 7 …;
· Geometric — a(n) = first term × common ratio^(n-1); first term 1 and ratio 2 give 1, 2, 4, 8 …;
· Fibonacci — both the 1st and 2nd terms take the first term value, and each later term equals the sum of the previous two;
· Lucas — the 1st term takes the first term value, the 2nd takes the difference/ratio value, and each later term equals the sum of the previous two (default 2, 1, 3, 4, 7, 11 …);
· Squares — a(n) = first term × n²;
· Triangular — a(n) = first term × n(n+1) ÷ 2.
Note: when the first term and difference are integers, all arithmetic uses big integers, so results beyond JavaScript's safe integer range, such as the 90th Fibonacci term, stay exact; with a decimal ratio, floating-point arithmetic is used and values are rounded to the chosen decimal places.
Supported sequence types:
· Arithmetic — a(n) = first term + (n-1) × common difference; first term 1 and difference 2 give 1, 3, 5, 7 …;
· Geometric — a(n) = first term × common ratio^(n-1); first term 1 and ratio 2 give 1, 2, 4, 8 …;
· Fibonacci — both the 1st and 2nd terms take the first term value, and each later term equals the sum of the previous two;
· Lucas — the 1st term takes the first term value, the 2nd takes the difference/ratio value, and each later term equals the sum of the previous two (default 2, 1, 3, 4, 7, 11 …);
· Squares — a(n) = first term × n²;
· Triangular — a(n) = first term × n(n+1) ÷ 2.
Note: when the first term and difference are integers, all arithmetic uses big integers, so results beyond JavaScript's safe integer range, such as the 90th Fibonacci term, stay exact; with a decimal ratio, floating-point arithmetic is used and values are rounded to the chosen decimal places.
How to use
- Choose the sequence type.
- Enter the first term and the common difference / ratio; geometric sequences also accept decimals, such as 0.5.
- Enter the number of terms (up to 200).
- Set the decimal places to control rounding for sequences such as geometric ones that produce decimals.
- Set the separator; the default \\n puts one term per line, and switching to a half-width comma joins them onto one line.
- Click Start; results appear in the text box and the table below (term index / value / difference from previous term / running sum), and the table can be downloaded as CSV.
Message board
All messages →-
No one has spoken up yet — want to go first?