What is a geometric sequence?

A sequence where each term is multiplied by a constant ratio (r). Example: 2, 6, 18, 54 — first term 2, ratio 3. Used to model exponential growth and compound interest.

What is the sum of an infinite geometric series?

If |r| < 1, the infinite sum = a₁ / (1 - r). Example: 1 + 0.5 + 0.25 + ... = 1 / (1 - 0.5) = 2. If |r| ≥ 1, the series diverges (no finite sum).

Geometric Sequence Calculator

Quick answer: Enter first term, common ratio, and number of terms to find the nth term and sum.

Calculate any geometric sequence: find the nth term, partial sum, and first 20 terms. A geometric sequence multiplies each term by a constant ratio.

Last reviewed: April 2026Report an error

First Term (a₁)

Common Ratio (r)

Number of Terms (n)

nth Term

128.00

a(8) = 128.00, sum = 255.00.

nth Term

128.00

Sum of n Terms

255.00

First 8 Terms

1.00, 2.00, 4.00, 8.00, 16.00, 32.00, 64.00, 128.00

How to Use This Geometric Sequence Calculator

1Enter the first term (a₁).
2Enter the common ratio (r — can be a fraction).
3Enter the number of terms (n).
4Read the nth term, sum, and first 20 terms.

Frequently Asked Questions

: A sequence where each term is multiplied by a constant ratio (r). Example: 2, 6, 18, 54 — first term 2, ratio 3. Used to model exponential growth and compound interest.
: If |r| < 1, the infinite sum = a₁ / (1 - r). Example: 1 + 0.5 + 0.25 + ... = 1 / (1 - 0.5) = 2. If |r| ≥ 1, the series diverges (no finite sum).

</> Embed this calculator on your website

<iframe src="https://calqpro.com/calculators/geometric-sequence-calculator" width="100%" height="600" frameborder="0" title="Calqpro Calculator" loading="lazy"></iframe>
<p>Powered by <a href="https://calqpro.com">Calqpro</a></p>

Geometric Sequence Calculator

How to Use This Geometric Sequence Calculator

Frequently Asked Questions

Related Calculators