← Math & statistics

Sequences & Series Calculator

Explore arithmetic and geometric sequences in one place: compute nth terms, partial sums, solve for unknown indices, infer a1 and d or r from two terms, and generate tables with instant step-by-step explanations.

Copy LaTeX or a shareable URL with one click (Alt+L / Alt+S shortcuts). Teacher mode highlights key reminders for lesson planning, and results update live with accessible status messages.

Other languages 日本語 | English | 简体中文 | 繁體中文 | 繁體中文(香港) | Español | Español (México) | Português (Brasil) | Português (Portugal) | Bahasa Indonesia | Tiếng Việt | 한국어 | Français | Deutsch | Italiano | Русский | हिन्दी | العربية | বাংলা | اردو | Türkçe | ไทย | Polski | Filipino | Bahasa Melayu | فارسی | Nederlands | Українська | עברית | Čeština

What you can do

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.

    What should I enter first?

    Start with the minimum required inputs shown above the calculate button, then keep optional settings at their defaults for a first pass. After getting a baseline, change one parameter at a time so you can explain which assumption moved the output.

    How precise are the results?

    The calculator keeps internal precision and rounds only for display. Small differences can still appear if another tool uses different constants, period conventions, or rounding rules. Align assumptions before comparing final values.

    Why can my result differ from another calculator?

    Many tools choose different defaults for units, rate basis, date-count logic, and sign conventions. Verify those defaults first. If differences remain, use the worked example and compare each intermediate step to locate the branch that diverges.

    How to use Sequences & Series Calculator effectively

    What this calculator does

    This page is for estimating outcomes by changing inputs in one controlled workflow. The model keeps your focus on variables, not output shape. Start with stable assumptions, then test sensitivity by changing one key input at a time to observe directional impact.

    Input meaning and unit policy

    Each input has an expected unit and a typical range. For reliable interpretation, check whether you are using the same unit system, period, and base assumptions across all runs. Unit mismatch is the most common source of unexpected drift in numeric results.

    Use-case sequence

    A practical sequence is: first run with defaults, then create a baseline log, then run one alternative scenario, and finally compare only the changed output metric. This sequence reduces cognitive load and prevents false pattern recognition in early experiments.

    Common mistakes to avoid

    Avoid changing too many variables at once, mixing incompatible data sources, and interpreting a one-time output without checking robustness. A single contradictory input can flip conclusions, so keep each experiment minimal and document assumptions as part of your note.

    Interpretation guidance

    Review both magnitude and direction. Direction tells you whether a strategy moves outcomes in the desired direction, while magnitude helps you judge practicality. If both agree, you can proceed; if not, rebuild the baseline and verify constraints before deciding.