Calculators
Geometric Sequence Calculator
Find the nth term and finite sum of a geometric sequence from its first term and common ratio, privately in your browser.
Find terms and finite sums for a constant ratio.
A geometric sequence multiplies each term by a constant ratio r. Its nth term is aₙ = a₁ × r^(n − 1). For r ≠ 1, the finite sum is Sₙ = a₁(1 − r^n)/(1 − r); when r = 1, Sₙ = n × a₁. Starting at 3 with ratio 2, ten terms end at 1536 and sum to 3069. Negative ratios alternate signs, zero ratios give zeros after the first term, and ratios between zero and one produce shrinking terms. Enter finite signed decimals or scientific notation and a whole term count from 1 to 10,000. The tool accumulates the finite sum directly with compensated summation and previews at most ten terms. Browser floating-point arithmetic can lose precision; results display up to 12 significant digits. Overflow and terms that underflow to zero are rejected. This tool does not calculate infinite series or infer ratios from lists. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How do I find the nth geometric term?
Use aₙ = a₁ × r^(n − 1). With first term 3 and ratio 2, the tenth term is 1536.
How is the finite sum calculated?
For r ≠ 1, Sₙ = a₁(1 − r^n)/(1 − r). When r = 1, use n × a₁. This calculator accumulates terms directly with compensated summation. Ten terms starting at 3 with ratio 2 sum to 3069.
Can the ratio be negative or zero?
Yes. Negative ratios alternate signs. A zero ratio leaves only the first term nonzero, while ratio one gives a constant sequence. The first term can also be negative or zero.
What limits and precision apply?
Enter finite signed numbers and 1 to 10,000 terms. Results use floating-point arithmetic and display up to 12 significant digits. Overflow and terms underflowing to zero are rejected. This calculates finite sums only; all data stays in your browser.