Solve sequence sums using common series rules and methods. Enter terms, ratio, or limits easily. See partial totals, formulas, tables, and exports with guidance.
| Series Type | Inputs | Formula | Partial Sum |
|---|---|---|---|
| Arithmetic | a = 4, d = 3, n = 8 | S_n = n/2 × [2a + (n - 1)d] | 116 |
| Geometric | a = 2, r = 3, n = 5 | S_n = a × (1 - r^n) / (1 - r) | 242 |
| Natural Numbers | n = 10 | S_n = n(n + 1) / 2 | 55 |
| Squares | n = 6 | S_n = n(n + 1)(2n + 1) / 6 | 91 |
| Cubes | n = 4 | S_n = [n(n + 1) / 2]² | 100 |
S_n = n/2 × [2a + (n - 1)d]
Use this when each term changes by a fixed difference.
S_n = a × (1 - r^n) / (1 - r), when r is not 1.
Use S_n = a × n when every term is equal.
S_n = n(n + 1) / 2
This sums consecutive counting numbers from 1 to n.
S_n = n(n + 1)(2n + 1) / 6
This adds squared values from 1² to n².
S_n = [n(n + 1) / 2]²
This adds cubic values from 1³ to n³.
Partial sum formulas help you add sequence terms quickly. They reduce long manual work. They also improve accuracy. Students use them in algebra and calculus. Analysts use them in finance and modeling. Developers use them in loops, tests, and simulations.
An arithmetic series grows by a fixed difference. A geometric series grows by a fixed ratio. These two patterns appear in many real problems. Salary steps often follow arithmetic growth. Compound change often follows geometric growth. A reliable partial sum formula calculator saves time in both cases.
Natural numbers, square numbers, and cube numbers also have direct formulas. These are classic sequence identities. They appear in sigma notation, proofs, and exam questions. They also support faster verification when you compare hand calculations with computed results.
This tool does more than display a final answer. It returns the partial sum, the nth term, the formula used, and a preview table of cumulative totals. That structure makes checking easy. You can review each step pattern before exporting your work.
The calculator supports decimal control. That helps when ratios or starting values are not whole numbers. The preview limit also keeps large sequences readable. For documentation, you can export the output as CSV or save the report as PDF. That is useful for homework records, class notes, and project files.
Use this partial sum formula calculator when you need fast series totals, clean formulas, and visible term growth. It is useful for revision, teaching, research, and general number analysis. It gives a clear result with less effort and fewer mistakes.
A partial sum is the total of the first n terms of a sequence or series. It stops at a chosen point instead of continuing forever.
Yes. Enter the first term, common difference, and number of terms. The calculator then returns the nth term and the arithmetic partial sum.
Yes. Enter the first term, common ratio, and number of terms. It uses the finite geometric sum formula and shows the result clearly.
When the ratio is 1, every term is the same. The sum becomes first term multiplied by the number of terms.
Yes. It supports natural numbers, squares, and cubes. These options are useful for classroom practice and quick identity checks.
The preview table helps you inspect term values and cumulative totals. It makes the output easier to verify and easier to teach.
CSV export lets you open the results in spreadsheet software. That is useful for reporting, record keeping, and further analysis.
Calculate the series first. Then press the PDF button. The page creates a downloadable report with summary values and term rows.
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.