How to use Arithmetic and Geometric Sequence Calculator
- Choose arithmetic or geometric and enter the first term.
- Enter the common difference or ratio and the positive term count.
- Review the nth term, finite sum and term list.
Example: Arithmetic and Geometric Sequence Calculator
Arithmetic and Geometric Sequence Calculator: Term 10 of the arithmetic sequence is 21, and the sum of the first 10 terms is 120.
Options
- First term
- The starting value is term 1. Arithmetic mode adds the common difference; geometric mode multiplies by the common ratio.
- Term count
- The list and sum include exactly the entered count. This is a finite sequence calculation, including when the ratio is zero or negative.
Supported inputs and limits
Where your input is processed
This tool processes your input in this browser. Your text and files are not uploaded to UseFreeTools. Check this tool's limits for anything it may save on your device.
Check the index used in the original problem
A formula that starts at index zero can describe the same values with different labels. This page uses one-based labels throughout. It does not infer a pattern from observations or claim convergence of an infinite geometric series.
Questions about Arithmetic and Geometric Sequence Calculator
Is the first term numbered zero or one?
One. The nth-term result uses the entered first term as a1.
Can a geometric ratio be zero or negative?
Supported finite calculations handle those values explicitly. A negative ratio alternates signs; zero makes terms after the first zero.
Does the tool find a pattern from a list?
No. You supply the arithmetic difference or geometric ratio.