Find missing sequence terms for savings, payments, and forecasts. Test arithmetic or geometric rules quickly. Get tables, totals, exports, and practical planning insight today.
| Scenario | Type | First Term | Difference or Ratio | Requested Index | Meaning |
|---|---|---|---|---|---|
| Monthly savings increase | Arithmetic | $1,000 | 250 | 12 | Deposit rises by a fixed amount. |
| Annual rent escalation | Arithmetic | $12,000 | 500 | 6 | Cost climbs evenly each year. |
| Investment growth | Geometric | $5,000 | 1.08 | 10 | Value compounds by 8% each term. |
| Sales forecast | Geometric | $20,000 | 1.05 | 8 | Revenue grows by 5% each period. |
| Step-up loan plan | Arithmetic | $700 | 50 | 15 | Installment increases steadily over time. |
The nth term formula is aₙ = a₁ + (n - 1)d.
The sum formula is Sₙ = n / 2 × [2a₁ + (n - 1)d].
The nth term formula is aₙ = a₁ × r^(n - 1).
If the ratio is not 1, the sum formula is Sₙ = a₁ × [(r^n - 1) / (r - 1)].
If the ratio equals 1, then Sₙ = n × a₁.
Arithmetic sequences fit step-up deposits, staged fees, and fixed payment increases.
Geometric sequences fit compound growth, inflation-adjusted forecasts, and recurring percentage changes.
Finance often uses repeated values. Those values may rise evenly. They may also grow by a constant rate. A sequence calculator helps you inspect that pattern fast. It shows where a plan starts. It also shows where the plan may end.
An arithmetic sequence adds the same amount each step. This is useful for salary steps, staged savings, rent ladders, and payment schedules. You can model a plan that grows by fixed currency units. That makes budgeting clearer. It also makes future cash flow checks easier.
A geometric sequence multiplies each term by the same ratio. This matches compound growth better. It is useful for investments, revenue forecasts, inflation effects, and balance projections. When you know the first value and the ratio, you can estimate future terms quickly. You can also compare aggressive and conservative scenarios.
This page does more than return one answer. It can calculate a target term. It can list a term range. It can total the first set of terms. It can also infer the missing rule from two known points. That is helpful when you already know two values from a report.
The output table helps you read each term clearly. You can inspect change from the previous term. You can review the running total too. That helps with cash planning, contribution tracking, and growth review. The export options are useful for sharing results with teams or clients. Use this tool when you need fast sequence checks without manual spreadsheets.
A term is one value in an ordered pattern. In finance, each term may represent a payment, deposit, balance, revenue figure, or forecast point.
Use it when the value changes by the same fixed amount each period. Examples include fixed yearly fee increases or step-up monthly savings.
Use it when the value changes by the same percentage or ratio each period. Compound investment growth is the common example.
Yes. Select the inference option. Enter two known indices and their values. The calculator derives the difference or ratio automatically.
That restriction keeps finance use realistic and avoids invalid real-number roots when deriving a ratio from spaced terms.
It is the cumulative sum of displayed terms. This is useful for checking total deposits, total payouts, or total forecasted amounts.
The target term gives one specific indexed value. The sum adds several terms together to show the combined total over time.
Yes. Use the CSV button for spreadsheet work. Use the PDF button for a simple shareable report with the summary and table.
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.