Arithmetic Sequence Calculator
Calculate nth term, sum, and generate complete arithmetic sequences instantly. Free online tool with 100% privacy - all calculations happen locally in your browser.
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. For example: 2, 5, 8, 11... has a common difference of 3.
How is the nth term calculated?
The nth term is calculated using the formula: aₙ = a₁ + (n-1)d, where a₁ is the first term and d is the common difference.
How is the sum of an arithmetic sequence calculated?
The sum of the first n terms is calculated using: Sₙ = n(a₁ + aₙ)/2, which is the average of the first and last term multiplied by the number of terms.
What is the common difference in an arithmetic sequence?
The common difference (d) is the constant value added to each term to get the next term. It can be positive, negative, or zero.
Can this calculator handle negative numbers?
Yes, this calculator supports any real numbers for the first term and common difference, including negative numbers and decimals.
Is my data sent to any server?
No. All calculations happen locally in your browser. Your data never leaves your device, ensuring 100% privacy.
How many terms can I generate?
You can generate up to 1000 terms at once. The calculator displays the first 500 terms in the sequence output.
What are some real-world applications of arithmetic sequences?
Arithmetic sequences appear in finance (simple interest), physics (uniform motion), construction (stairs, ladders), and many other fields where linear patterns occur.
Can I use this calculator for homework or exams?
Yes, this is an excellent tool for students learning about sequences and series. It helps verify calculations and understand the formulas.
What's the difference between arithmetic and geometric sequences?
In arithmetic sequences, the difference between terms is constant. In geometric sequences, the ratio between consecutive terms is constant.
How to Use Arithmetic Sequence Calculator
This arithmetic sequence calculator finds the nth term and the sum of the series, and lists every term for you. Everything runs locally in your browser, so no data is ever uploaded.
- Type the starting value into the First Term (a₁) field — this is where your sequence begins.
- Enter the fixed step between consecutive numbers in the Common Diff (d) field, e.g. 3 for 2, 5, 8, 11.
- Set how many entries you want in the Terms (n) field, such as 10 or 50.
- Read the nth term and total sum from the results, then copy the full sequence if you need it.
Negative and decimal values are fine — a₁ = 0.5 with d = -2 produces a valid decreasing sequence.
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