What you can do
- Arithmetic (AS) and geometric (GS) nth terms, interval sums, solving for n or k, and two-term inference
- Generate copy-ready tables of t_n and cumulative S_n for any interval
- Display every substitution in a dedicated “How it’s calculated” column for classroom-friendly steps
- Share URLs, copy LaTeX, toggle teacher notes, and load comments on demand
Mode
Results
How it's calculated
FAQ
How are logarithms handled when solving geometric terms?
For r > 0 we solve n = n0 + log(T/a1) / log(r). For r < 0 we additionally enforce |r|^k = |T/a1| and (-1)^k = sign(T/a1); otherwise the tool reports that the parity constraint fails.
Can I export the generated table?
Yes. After computing, click “Copy as CSV” to push a tidy n,t_n,S_n table to your clipboard, ready for spreadsheets or LMS uploads.
When is the infinite geometric sum available?
Use the sum to infinity mode only when the common ratio satisfies |r| < 1. If |r| is 1 or greater, the tool reports that the series does not converge instead of forcing a finite answer.
How do I solve for a missing index or term?
Choose the arithmetic or geometric solve mode that matches your known values, then compare the step log with the formula shown in the result. Negative geometric ratios also need the sign/parity check shown above.
What should I check before exporting a table?
Confirm the start index, end index, and whether the table should show terms, cumulative sums, or both. The CSV copy uses the displayed interval so it is ready for spreadsheets and lesson materials.
How to use Sequences & Series Calculator effectively
Choose the sequence model first
Start by deciding whether the data follows an arithmetic difference or a geometric ratio. The mode controls which fields appear, which formula is logged, and whether an infinite-sum check is meaningful.
Use the step log as the source of truth
Each run shows the substitution path for nth terms, partial sums, inverse solving, or two-point inference. Read the log before copying results so an index shift, negative ratio, or finite interval does not hide inside a rounded answer.
Export only after checking the interval
For tables, verify n0, N, and the cumulative sum column before copying CSV or LaTeX. This keeps classroom examples and spreadsheet imports aligned with the exact interval you solved.