How to use the arithmetic sequence calculator
Use the calculator to find a requested term and the sum through that term. Select the known values, enter the required numbers, choose Which term to solve for (n), and select Calculate.
- Select First term & common difference or Two known terms.
- Enter the values shown for that mode and a positive whole number in Which term to solve for (n).
- Select Calculate to show the result and calculation steps.
- Use Copy result or Download result (.txt) to save the displayed result.
Choose the known information
Select First term & common difference when you know the first term and the amount added to each term. Select Two known terms when you know two term values and their positions; the positions must be different positive whole numbers.
In either mode, enter the target position in Which term to solve for (n). Changing the known-information mode hides the current result.
Review the calculated term and sum
After a successful calculation, the result shows the requested term, the sum through n, and the calculation steps. The displayed sum formula is S_n = n / 2 × (2a_1 + (n - 1) × d). The sequence preview lists the first terms when available.
Input format and calculation limits
- Enter values as plain decimal text, with an optional leading minus sign. Exponent notation, a leading plus sign, and other number formats are rejected.
- Term positions must be positive whole numbers, and the two known-term positions must be different.
nand known-term positions cannot exceed1,000,000,000.- If
nis greater than 50, the sequence preview lists only the first 50 terms. - Use consistent units as plain numbers if needed. The calculator does not label or convert units.
Copying, downloading, and reset behavior
Select Copy result to copy the result when clipboard access succeeds. If copying fails, the calculator displays a message asking you to select and copy it manually. Select Download result (.txt) to save the result as a text file. Reset clears the calculation and hides the result.
Privacy and data handling
The calculator script performs the calculation locally and does not upload the values you enter. The surrounding site still loads Ahrefs and Google Analytics and records page views server-side.
Frequently asked questions
What is an arithmetic sequence?
An arithmetic sequence is a list of numbers where each term after the first is found by adding the same common difference to the term before it.
What is the formula for the nth term?
The nth term is a_n = a_1 + (n - 1) * d, where a_1 is the first term and d is the common difference.
What is the formula for the sum?
The calculator displays S_n = n / 2 * (2 * a_1 + (n - 1) * d) for the sum through term n.
Can I use two known terms?
Yes. Select Two known terms, enter their distinct positive whole-number positions and values, then choose Calculate.
Does it accept negative numbers or decimals?
Yes. Value fields accept plain decimal text with an optional leading minus sign. Positions must be positive whole numbers.