Arithmetic Sequence Calculator
Find the nth term and the sum of an arithmetic sequence from the first term, common difference and term count. Lists the terms too.
Last reviewed by the Radiatus Cloud team
Compute the nth term and the sum of an arithmetic sequence a, a+d, a+2d, ...
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Work with arithmetic sequences
An arithmetic sequence is a list of numbers in which each term increases by a fixed amount called the common difference. Starting from the first term a and adding the difference d each step gives a, a plus d, a plus two d, and so on. This calculator finds the nth term using the formula a plus n minus one times d, and the sum of the first n terms using n divided by two times twice a plus n minus one times d.
It also lists the terms so you can see the pattern directly, which is useful for checking homework or spotting where a sequence reaches a particular value.
Where arithmetic sequences appear
Arithmetic progressions model steady, linear change: seats in each successive row of a theatre, equal monthly savings, the stacking of objects in layers, or the degrees marked on a scale. Students meet them throughout algebra, and the sum formula, attributed to the young Gauss, is a classic shortcut for adding a long run of evenly spaced numbers.
Enter any real first term and difference, including negatives and decimals, to model decreasing sequences as well. All calculation runs locally in your browser.
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Frequently Asked Questions
What is the common difference?
It is the fixed amount added to each term to get the next one. A positive difference increases the sequence, a negative difference decreases it.
How is the nth term found?
With the formula a plus n minus one times d, where a is the first term, d is the common difference and n is the position you want.
How is the sum calculated?
The sum of the first n terms equals n over two times the quantity twice the first term plus n minus one times the common difference.
Why are only the first terms listed?
To keep the output readable, the term list shows up to fifty values. The nth term and sum are still calculated exactly for any n.
Can the difference be a decimal?
Yes. The first term and common difference can be any real numbers, including decimals and negatives.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter the first term, common difference and number of terms to get the nth term and sum.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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