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
Sequence Analyzer lists the classic sequences and reveals how they grow — the Difference and Running Total columns are the two most useful angles when analysing a sequence.
Supported types:
· Arithmetic — a(n) = first + (n-1) × difference, e.g. first 1 with difference 2 gives 1, 3, 5, 7 …;
· Geometric — a(n) = first × ratio^(n-1), e.g. first 1 with ratio 2 gives 1, 2, 4, 8 …;
· Fibonacci — terms 1 and 2 both equal the first term, then each term is the sum of the previous two;
· Lucas — term 1 is the first term, term 2 is the difference/ratio value, then each term is the sum of the previous two (defaults give 2, 1, 3, 4, 7, 11 …);
· Square — a(n) = first × n²;
· Triangular — a(n) = first × n(n+1) ÷ 2.
Steps:
1. Pick the sequence type;
2. Enter the First Term and the Difference / Ratio — geometric sequences accept decimals such as 0.5;
3. Enter the Term Count (up to 200);
4. Set Decimal Places to control how many decimals are kept for sequences such as geometric ones;
5. Set the separator — the default \n puts one term per line, a comma joins them onto one line;
6. Click Run. Results appear in the text box and in the table below (index / value / difference / running total), with CSV export.
Note: when the first term and the difference are both integers, everything is computed with big integers, so results like the 90th Fibonacci number stay exact even beyond JavaScript's safe integer range; a decimal ratio switches to floating point and is rounded to the chosen number of decimal places.
Supported types:
· Arithmetic — a(n) = first + (n-1) × difference, e.g. first 1 with difference 2 gives 1, 3, 5, 7 …;
· Geometric — a(n) = first × ratio^(n-1), e.g. first 1 with ratio 2 gives 1, 2, 4, 8 …;
· Fibonacci — terms 1 and 2 both equal the first term, then each term is the sum of the previous two;
· Lucas — term 1 is the first term, term 2 is the difference/ratio value, then each term is the sum of the previous two (defaults give 2, 1, 3, 4, 7, 11 …);
· Square — a(n) = first × n²;
· Triangular — a(n) = first × n(n+1) ÷ 2.
Steps:
1. Pick the sequence type;
2. Enter the First Term and the Difference / Ratio — geometric sequences accept decimals such as 0.5;
3. Enter the Term Count (up to 200);
4. Set Decimal Places to control how many decimals are kept for sequences such as geometric ones;
5. Set the separator — the default \n puts one term per line, a comma joins them onto one line;
6. Click Run. Results appear in the text box and in the table below (index / value / difference / running total), with CSV export.
Note: when the first term and the difference are both integers, everything is computed with big integers, so results like the 90th Fibonacci number stay exact even beyond JavaScript's safe integer range; a decimal ratio switches to floating point and is rounded to the chosen number of decimal places.
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