Calculator tool
How this calculator works
Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.
Two Common Kinds of Sequences
An arithmetic sequence adds the same amount each time. A geometric sequence multiplies by the same amount each time.
| Type | Example | Pattern |
|---|---|---|
| Arithmetic | 3, 7, 11, 15 | add 4 |
| Geometric | 2, 6, 18, 54 | multiply by 3 |
How to Recognize the Pattern
If the gap between nearby terms stays the same, the sequence is arithmetic. If the ratio between nearby nonzero terms stays the same, it is geometric.
Why the Difference Matters
The two patterns grow very differently. Adding 4 each step stays steady, but multiplying by 3 grows much faster. Choose the correct pattern before using later terms or making predictions.
What the Calculator Uses
For arithmetic sequences it uses a starting term and a common difference. For geometric sequences it uses a starting term and a common ratio.
Frequently asked questions
What is the difference between arithmetic and geometric sequences?
Arithmetic sequences add a constant difference, while geometric sequences multiply by a constant ratio.
How do I find the nth arithmetic term?
Use , where is the first term and is the common difference.
How do I find the nth geometric term?
Use , where is the common ratio and is the term position.
Can every pattern be modeled by these two sequence types?
No. Some patterns are neither arithmetic nor geometric and need a different rule.
