Find arithmetic series totals with confidence. Switch modes, validate inputs, and inspect every important step. Export results, compare examples, and learn the underlying formula.
Nth term: an = a + (n - 1)d
Sum using first term and difference: S = n/2 × [2a + (n - 1)d]
Sum using first and last term: S = n(a + l)/2
Average term: Average = (a + l)/2
This calculator uses the term-count formula when you know n. It switches to the first-and-last-term formula when you solve from the last term.
| First Term | Difference | Terms | Last Term | Sum |
|---|---|---|---|---|
| 3 | 2 | 10 | 21 | 120 |
| 12 | -1.5 | 8 | 1.5 | 54 |
| 5 | 0 | 6 | 5 | 30 |
| 1.2 | 0.8 | 9 | 7.6 | 39.6 |
An arithmetic series sum calculator helps you add equally spaced terms quickly. Every term changes by one fixed common difference. That pattern is called an arithmetic progression. You can use this tool for classwork, finance practice, exam revision, and sequence analysis. It removes repeated manual addition. It also reduces avoidable errors. This page calculates the total sum, the last term, the average term, and a short preview of the sequence.
Arithmetic series appear in many real problems. Weekly savings plans often increase by one constant amount. Seating rows can grow by a steady count. Production targets can rise in fixed steps. Salary models and installment plans may follow similar patterns. In maths, these sequences build number sense. They also support algebra, statistics, and discrete problem solving. A reliable arithmetic progression calculator saves time when you need quick checking.
The classic arithmetic series formula is direct and efficient. If you know the first term, common difference, and number of terms, use S = n/2 × [2a + (n - 1)d]. If you know the first term and last term, use S = n(a + l)/2. Both formulas return the same total. This calculator checks that relationship. It also finds the nth term, which helps confirm that your sequence inputs are valid.
The result section is more than a final total. It shows the series type, average term, and middle term when one exists. That makes review easier. A preview list shows early terms in order. You can compare them with notebook work or classroom examples. The export tools are useful for records and reporting. Use the CSV file for spreadsheets. Use the PDF file for sharing or printing. This makes the tool practical and fast.
An arithmetic series is the sum of terms from an arithmetic sequence. The difference between consecutive terms stays constant throughout the pattern.
The common difference is the fixed amount added or subtracted to move from one term to the next. It controls whether the series rises, falls, or stays constant.
Use last-term mode when you know the first term, common difference, and final term, but you do not know how many terms are in the series.
Yes. A negative common difference creates a decreasing arithmetic sequence. The calculator still finds the correct term count, last term, and total sum.
Yes, in term-count mode. A zero difference means every term is identical. In last-term mode, zero difference can become ambiguous unless the term count is already known.
The last term must land on a whole-number term position. If it does not, the entered values do not form a valid arithmetic series with an integer number of terms.
The average term helps verify the structure of the series. In arithmetic series, the average equals the midpoint between the first and last terms.
Yes. The page includes CSV and PDF download options. You can save result summaries and also export the example table for records or review.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.