Sequence Calculator with Steps & Graphs
Enter terms, an explicit formula, or a recurrence. Explore possible patterns, calculate terms, inspect differences, and visualize the sequence.
Define your sequence
Choose an input method, then select Analyze sequence.
Try an example
Select one to fill the form.
Step-by-step solution
Difference table
Constant first, second, or higher differences suggest a polynomial pattern.
Analysis
Ready to analyze
Formula detection depends on the terms provided.
Finite sums and applicable infinite geometric sums will appear here.
Sequence graph
Each point represents a discrete term (n, an).
Points are separate by default because a sequence is defined at integer indices.
Terms & partial sums
| n | an | Δan | Sn |
|---|---|---|---|
| No terms calculated yet. | |||
Sequence properties
- Monotonicity
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- Boundedness
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- Convergence
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- Limit
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Observed behavior from plotted terms alone cannot establish a limit or bound. The analysis will distinguish estimates from proved results.
Recurrence breakdown
Save your results
Take the terms, graph, and solution with you.
About sequence calculations
How do I find the nth term?
For arithmetic sequences, use an = a1 + (n − 1)d. For geometric sequences, use an = a1rn−1. Constant higher differences can suggest a polynomial formula.
Does a difference table prove the formula?
No. Any finite set of terms can agree with multiple formulas. The tool presents a simple fitting rule and the steps used to find it.
Why are the graph points separate?
The index n is an integer. A continuous line between points is only a visual aid and does not define additional sequence terms.
What is the difference between a sequence and a series?
A sequence lists terms a1, a2, …. A series adds those terms. Its nth partial sum is Sn = a1 + ⋯ + an.