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.

Hisabati

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

🔒

100% Bure

Hakuna usajili

✓

Sahihi

Mifumo iliyothibitishwa

⚡

Papo Hapo

Matokeo unapoandika

📱

Tayari kwa Simu

Vifaa vyote

Geometric Sequence Calculator

Geometric Sequence Calculator

Ni nini Geometric Sequence Calculator?

Mfumo

Maelezo ya kigezo

Jinsi ya Geometric Sequence Calculator

Mifano Iliyotatuliwa

Matumizi ya vitendo

Geometric Sum Sₙ for a₁=1

Maswali yanayoulizwa mara kwa mara

Mipangilio

Geometric Sequence Calculator