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Sum of Series Calculator.

Sum a finite arithmetic or geometric series; the selected family is shown explicitly.

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01

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Results update as you type.

lastTerm: 11

lastTerm

0.00000000
sum: 26

sum

0.00000000

Results update automatically as you type.

Sum a finite arithmetic or geometric series; the selected family is shown explicitly.

Use Cases

Summing a sequence of payments

Calculate the total amount of a series of payments that increase by a fixed amount (arithmetic) or by a fixed percentage (geometric).

Example: Sum of 12 monthly payments starting at $100 and increasing by $10 each month.

Totaling a geometric growth pattern

Find the total of a series that grows by a constant factor, such as population growth or compound interest over a fixed number of periods.

Example: Sum of 5 terms starting at 1000 with a ratio of 1.5.

Frequently Asked Questions

What is the difference between an arithmetic and a geometric series?
An arithmetic series has a constant difference between consecutive terms (e.g., 2, 5, 8, ...). A geometric series has a constant ratio between consecutive terms (e.g., 2, 6, 18, ...). This calculator lets you choose the series type and then uses the appropriate formula.
How do I find the sum of an arithmetic series?
For an arithmetic series, the sum is calculated using the formula: S = n/2 * (2a + (n-1)d), where 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms. Simply enter these values into the calculator.
How do I find the sum of a geometric series?
For a geometric series, the sum is calculated using the formula: S = a * (1 - r^n) / (1 - r), where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms. Enter these values to get the sum.

Tips & Common Mistakes

Tips

  • Ensure the number of terms is a positive integer. The calculator expects a whole number for the count of terms.
  • For a geometric series, the common ratio should not be 1, as the formula becomes undefined. If the ratio is 1, the sum is simply the first term times the number of terms.
  • Double-check the sign of the common difference or ratio. A negative difference or ratio will alternate the signs of terms, affecting the sum.
  • Use the calculator to verify your manual calculations, especially for series with many terms.

Common Mistakes to Avoid

  • Confusing the common difference (arithmetic) with the common ratio (geometric). Make sure you select the correct series type.
  • Entering the number of terms incorrectly, such as using the last term's index instead of the total count of terms.
  • Forgetting that the sum formula for a geometric series requires the ratio not equal to 1. If you enter 1, the result will be incorrect.

Last updated: August 13, 2026