Math & Science100% Free Tool

Free Geometric Sequence & Series Calculator (Finite & Infinite Sum) Online

Calculate the Nth term a_n = a₁ × r^(n-1), common ratio r, finite series sum, and infinite converging geometric sum S_∞. — 100% free online utility, zero sign-up, zero paywalls, and private client-side processing.

100% Client-Side0ms Latency
Algebraic & Polynomial Solverax² + bx + c = 0
Roots of Equationx₁ = 3.000, x₂ = 2.000
Discriminant (Δ)1
Parabola Vertex(2.50, -0.25)
Axis of Symmetryx = 2.50

How It Works

1

Enter First Term (a₁)

Input sequence start value.

2

Enter Common Ratio (r)

Input multiplier ratio between terms.

3

Inspect Convergence

If |r| < 1, evaluates infinite converging sum S_∞ = a₁ / (1 - r).

Frequently Asked Questions

Only when the absolute value of the common ratio is strictly less than 1 (|r| < 1).

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