How does the Geometric Sequence Calculator work?

aₙ = a₁ × rⁿ⁻¹ Then: Sum of n terms: Sₙ = a₁(1−rⁿ)/(1−r) Then: Sum to infinity (|r|<1): S∞ = a₁/(1−r) Then: Ratio r = aₙ/aₙ₋₁.

Can you give an example of how to use the Geometric Sequence Calculator?

Example: Input a₁ = 2, r = 3, 5 terms gives a result of 2, 6, 18, 54, 162 — Sum = 242.

Is the Geometric Sequence Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Geometric Sequence Calculator?

Our Geometric Sequence Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Toán học

Geometric Sequence Calculator

First Term (a₁)

Common Ratio (r)

Terms (n)

A geometric sequence has each term as a constant multiple (common ratio r) of the previous term. Geometric sequences model exponential growth, compound interest, and population dynamics.

Symbol	Name	Unit	Description
a₁	first term	—	—
r	common ratio	—	ratio of each term to the previous
n	number of terms	—	—
aₙ	nth term	—	—
Sₙ	sum of first n terms	—	—

r	S₅	S₁₀	S∞
0.5	1.9375	1.999	2
0.9	4.095	6.513	10
2	31	1023	∞
3	121	29524	∞

References

›Geometric sequences — Khan Academy

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Geometric Sequence Calculator

Geometric Sequence Calculator

Là gì Geometric Sequence Calculator?

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Chú giải biến

Cách Geometric Sequence Calculator

Ví dụ có lời giải

Ứng dụng thực tế

Geometric Sum Sₙ for a₁=1

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Geometric Sequence Calculator