Number Sequence Tool
Explore arithmetic, geometric, recurrence, prime, polynomial and other number sequences with configurable starting indices and term counts. View formulas, interactive charts, running sums, descriptive statistics and indexed tables, then export sequence data in several formats.
| Index (n) | Term (aₙ) | Running sum | Change |
|---|
Table of Contents
Highlights
- Eleven sequence types, from arithmetic progressions to polynomials
- Adjustable starting index and 2–200 displayed terms
- Interactive line, bar and scatter sequence charts
- Running totals, mean, range and indexed term table
- Export results as CSV, JSON, TXT or chart PNG
How Number Sequence Tool Works?
A number sequence assigns a value to each positive integer index n. Select a sequence type, specify its applicable parameters, choose a start index and generate between 2 and 200 consecutive terms. The displayed window begins at the chosen index, rather than always at the first term. Decimal places control display rounding, not the underlying calculations.
For an arithmetic progression with first term a and difference d:
For a geometric progression with ratio r:
The custom Fibonacci recurrence uses two entered starting terms, whereas the Lucas sequence starts with 2 and 1. In both cases, each later term is the sum of the preceding two terms.
Other supported sequences use these term rules:
| Sequence | Term at index n |
|---|---|
| Prime numbers | The nth prime, starting with 2 |
| Squares / cubes | n2 / n3 |
| Triangular numbers | n(n + 1) / 2 |
| Factorials | n! |
| Powers | a × bn − 1, with entered first term a and base b |
| Polynomial | An3 + Bn2 + Cn + D |
The results show the first and last displayed terms, total, mean, minimum and maximum. The table includes each index, term, cumulative sum within the displayed window, and change from the previous displayed term; the first change is blank. Switch the interactive graph between line, bar and scatter views, inspect points by hovering or tapping, and export CSV, JSON, TXT or chart PNG.
For example, first term 3 and common difference 4 produce 3, 7, 11, 15, 19 and so on. The first 20 terms end at 79 and sum to 820.
Practical Use Cases
Students: Explore arithmetic and geometric patterns, compare consecutive differences, and inspect indexed terms while practising algebra.
Teachers: Demonstrate Fibonacci and Lucas recurrences, show how sequences evolve on different graph styles, and export term tables for exercises.
Programmers: Generate primes, factorials, squares, cubes and powers as reference datasets, then download the indexed results in CSV or JSON.
Data analysts: Examine simple polynomial trends and compare minima, maxima, means and cumulative totals across a selected range of indices.
Maths enthusiasts: Investigate triangular numbers, explore non-standard recurrence seeds and see how changing parameters affects growth or oscillation.
Accuracy and Limitations
Calculations use JavaScript double-precision floating-point numbers, so large integers and decimal results may lose exact precision; the chosen 0, 2, 4, 6 or 10 decimal places affect presentation only. The tool accepts indices from 1 to 100,000 and 2–200 displayed terms, but limits primes to a final index of 100,200, factorials to 170!, and Fibonacci/Lucas sequences to a final index of 1,400. Values whose magnitude exceeds 10290 are rejected. Running sums and changes are calculated only for the displayed window; a non-finite or excessively large result triggers an error. The chart is an illustrative plot of the computed terms, not a proof of a pattern.
