Arithmetic Sequence Calculator
Work with arithmetic sequences — find terms and sums.
Adding the same each step
An arithmetic sequence increases by a constant amount each step — like 3, 7, 11, 15, adding four each time. This finds any term and the sum of a range of terms, for sequences that grow by a fixed difference.
Enter the sequence details to find terms or the sum.
The clever way to sum them
Finding a distant term is easy — start value plus the common difference times however many steps — but the elegant part is summing a long arithmetic sequence. Rather than adding every term, there is a shortcut, famously rediscovered by a young Gauss: pair the first term with the last, the second with the second-last, and so on, and every pair sums to the same total, so the whole sum is that pair-total times the number of pairs. This turns adding a hundred numbers into a single multiplication. Arithmetic sequences model anything that changes by a steady amount — regular savings, evenly-spaced rows, steady accumulation — and the summing trick is one of the most satisfying shortcuts in elementary maths.
Questions & answers
What makes a sequence arithmetic?
Each term increases by the same constant amount, the common difference — like 3, 7, 11, 15, adding four each time.
How do you sum a long arithmetic sequence quickly?
Pair the first and last terms, second and second-last, and so on — every pair sums to the same total, so multiply that by the number of pairs.
Is anything uploaded?
No. The calculation happens in your browser.