Choose arithmetic or geometric.
Algebra Calculator
Sequence & Series Calculator
Find the nth term, sum, and opening terms of an arithmetic or geometric sequence.
Instant answer
Formula breakdown
Browser-based
Mobile friendly
Interactive calculator
Enter your values
Use the example values or replace them with your own. Required validation happens before the calculation.
Ready
Calculated answer
Result
Simple workflow
How to use the Sequence & Series Calculator
Follow these steps to get a reliable result and understand how it was produced.
Enter the first term, common change, and n.
Calculate the nth term, finite sum, and sample terms.
Understanding the calculation
Arithmetic sequences add a fixed difference. Geometric sequences multiply by a fixed ratio.
Arithmetic: aₙ=a₁+(n−1)d; Geometric: aₙ=a₁r^(n−1)The result panel substitutes your numbers into this relationship and shows the important intermediate values.
Common uses
- Pattern and progression study
- Savings and growth models
- Series homework checks
Accuracy tips
- For arithmetic sequences, change means difference d.
- For geometric sequences, change means ratio r.
- Large geometric sequences may grow beyond normal number limits.
Helpful answers
Sequence & Series Calculator FAQs
Important details about formulas, inputs, limitations, and result interpretation.
What is an arithmetic sequence?
Each term is formed by adding the same difference to the previous term.
What is a geometric sequence?
Each term is formed by multiplying the previous term by the same ratio.
Does the calculator handle a ratio of 1?
Yes. The geometric sum then equals first term multiplied by n.
Why is n limited?
The limit prevents impractical output and extreme numeric overflow.