Geometric Sequence Calculator
Enter the first term, common ratio, and which term number you want to find the nth term and the sum of the first n terms.
How geometric sequences work
A geometric sequence is a list of numbers where each term is found by multiplying the one before it by a fixed value, the common ratio (r). The nth term is found as aₙ = a₁ × r^(n−1), where a₁ is the first term.
The sum of the first n terms is Sₙ = a₁ × (1 − rⁿ) / (1 − r) for any ratio other than 1 (if r = 1, every term is identical and the sum is simply a₁ × n).
Frequently asked questions
What's an example of a geometric sequence?
2, 6, 18, 54, ... is geometric with a common ratio of 3 — each term is 3 times the one before it.
What happens if the ratio is a fraction between 0 and 1?
The sequence shrinks toward zero — each term is smaller than the one before, like 100, 50, 25, 12.5, ... with a ratio of 0.5.
What if the common ratio is negative?
The sequence alternates between positive and negative values — for example, with a₁=1 and r=−2, the sequence is 1, −2, 4, −8, 16, ...