Integer Step Calculator
Sequence and Series Calculator works out nth term aₙ and Sum of the first n terms Sₙ from Sequence type, First term a₁ and Second term a₂. The default figures on this page give nth term aₙ of 10; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- Common difference d = 1.
- a_10 = 1 + (10 - 1)(1) = 10.
- S_10 = (10/2)(a_1 + a_10) = (10/2)(1 + 10) = 55.
Listed termstable
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the Sequence and Series Calculator calculates
Computes the nth term, the listed terms and the partial or infinite sum of an arithmetic, geometric, harmonic or Fibonacci-style sequence.
How to use this Sequence and Series Calculator
Enter Sequence type, First term a₁, Second term a₂ and Common difference d. Nth term aₙ updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind nth term aₙ, Sum of the first n terms Sₙ and Infinite sum S∞.
The method follows NIST Digital Library of Mathematical Functions, section 26.1 (finite sums and series), OEIS A000045, Fibonacci numbers and Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, chapter on sequences and series.
Arithmetic a1=3, d=5, n=10 example
With Sequence type: arithmetic, First term a₁: 3, Common difference d: 5, Term number n: 10, the calculator returns nth term aₙ: 48, Sum of the first n terms Sₙ: 255. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects nth term aₙ, Sum of the first n terms Sₙ and Infinite sum S∞. The inputs you can vary are Sequence type, First term a₁, Second term a₂, Common difference d, Common ratio r and Term number n.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
Is there a calculator that shows step by step?
Computes the nth term, the listed terms and the partial or infinite sum of an arithmetic, geometric, harmonic or Fibonacci-style sequence. On the figures this page opens with — first term a₁ 3 and common difference d 5 — the nth term aₙ is 10. Put your own figures in their place and the working updates beside the result.
How to do integers step by step?
Computes the nth term, the listed terms and the partial or infinite sum of an arithmetic, geometric, harmonic or Fibonacci-style sequence. Open “How this is worked out” beside the result to see each step for your own figures.
Can you provide a division calculator with steps?
It needs Sequence type, First term a₁, Second term a₂, Common difference d, Common ratio r and Term number n. Nothing else is required, and the figures stay in your browser.
What information do I need for the Sequence and Series Calculator?
You need Sequence type, First term a₁, Second term a₂, Common difference d, Common ratio r, Term number n and Terms to list. The page opens with default figures that give nth term aₙ of 10, so you can see the scale before entering your own.
What does this Sequence and Series Calculator show?
It shows nth term aₙ, Sum of the first n terms Sₙ, Infinite sum S∞, Listed terms, Explicit (closed) formula, Recursive formula, Sum formula and Series converges, with the working and any warnings for your entries.
Can I check how the Sequence and Series Calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.