What types of sequences does this calculator support?

Commonly arithmetic and geometric sequences.

How is the nth term of an arithmetic sequence calculated?

First term + (n−1) × common difference.

How is the nth term of a geometric sequence calculated?

First term × (common ratio)^(n−1).

Sequence Calculator | CalculatorLabs.net

Sequence Calculator

Find any term and the running sum of an arithmetic or geometric sequence.

What Is the Sequence Calculator?

This calculator finds any term and the running sum of an arithmetic sequence (constant difference between terms) or a geometric sequence (constant ratio between terms).

Formula

Arithmetic: aₙ = a₁ + (n−1)d, and Sum = n/2 × (2a₁ + (n−1)d). Geometric: aₙ = a₁ × rⁿ⁻¹, and Sum = a₁ × (rⁿ − 1) ÷ (r − 1) for r ≠ 1.

How to Use This Calculator

Choose arithmetic or geometric.
Enter the first term (a₁).
Enter the common difference (arithmetic) or common ratio (geometric).
Enter which term number (n) you want to find.
Click Calculate to see the n-th term and the sum of the first n terms.

Worked Example

For the arithmetic sequence 3, 7, 11, 15... (a₁=3, d=4), the 10th term is 39 (3 + 9×4), and the sum of the first 10 terms is 210.

Tips

For geometric sequences, a ratio between −1 and 1 (excluding 0) means the terms shrink toward zero as n grows, while a ratio greater than 1 means they grow without bound.