When to use this calculator
Find a term in a sequence multiplied by a fixed ratio each step. Use a whole-number term position. This model uses positive common ratios.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Geometric Sequence Ratio Calculator: Recover a positive common ratio from two terms of a geometric sequence.
PUTTING IT INTO PRACTICE
Geometric Sequence: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| First term | 2 |
| Common ratio | 3 |
| Term number (integer) | 5 |
| Result | 162 |
- Check the input labels and enter the example values above.
- Apply the relationship: Term = first × ratio^(n − 1).
- The result is 162 , rounded for display.
How to interpret your result
Use a whole-number term position. This model uses positive common ratios.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
How do I use the geometric sequence calculator?
Enter first term, common ratio, term number (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Term = first × ratio^(n − 1).
What should I check before using the result?
Use a whole-number term position. This model uses positive common ratios.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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