Sequence & Series Calculator interactive tool
n-th term aₙ
14.0000
Sum of first n terms Sₙ
40.0000
This sequence & series calculator uses the standard formulas for arithmetic and geometric sequences to find the n-th term and the partial sum.
What Is Sequence & Series?
A sequence & series calculator for arithmetic and geometric sequences computes n‑th terms and partial sums Sₙ. It's a convenient way to check answers in algebra and precalculus.
Arithmetic vs. Geometric Behavior
Arithmetic sequences grow (or shrink) linearly with a constant difference d, while geometric sequences grow multiplicatively with a constant ratio r. This calculator applies the standard closed‑form formulas so you can quickly see how different values of d or r change long‑term growth and total sums.
How To Use the Sequence & Series Calculator
- Choose whether you want to work with an arithmetic sequence or a geometric sequence.
- Enter the first term a₁, the common difference d (for arithmetic) or common ratio r (for geometric), and the number of terms n.
- The sequence & series calculator will compute the n-th term aₙ using the appropriate closed-form formula.
- It will also compute the partial sum Sₙ, the sum of the first n terms in the sequence.
- Use the Example button to load a typical arithmetic or geometric sequence, or Reset to clear the inputs.
Arithmetic and geometric sequence terms
This sequence and series calculator finds nth terms and partial sums for arithmetic and geometric sequences. Enter the first term and difference or ratio to compare the formula and resulting sum.
Need the formula or convention behind this result? Read the calculator methods and assumptions.