Geometric Sequence Calculator

Use our free geometric sequence calculator to find the nth term aₙ, common ratio r, determine n from aₙ, and generate the sequence.

Math

Mode

First Term (a₁)

Common Ratio (r)

Position (n)

nth Term (aₙ)

Formula

A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant r (the common ratio).

aₙ = a₁ × r^(n−1)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select a mode.
2To find aₙ: enter a₁, r, n.
3To find r: enter a₁, aₙ, n.
4To find n: enter a₁, r, aₙ.
5Click Calculate.

Examples

a₁=2, r=3, n=6

1.a₆ = 2 × 3⁵ = 2 × 243 = 486
2.Sequence: 2,6,18,54,162,486

Result: 486

Find r given a₁=2, a₆=486

1.r = (486/2)^(1/5) = 243^(0.2) = 3

Result: 3

Find n given a₁=2, r=3, aₙ=486

1.n = log(486/2)/log(3) + 1 = 6

Result: 6

Frequently Asked Questions

A sequence where each term is multiplied by a constant r.

aₙ = a₁ × rⁿ⁻¹.

Terms alternate in sign.

The common ratio.

Terms get smaller toward zero.

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CalculateMe Team

Last updated: 2026-07-14

Geometric Sequence Calculator

Formula

How It Works

Examples

a₁=2, r=3, n=6

Find r given a₁=2, a₆=486

Find n given a₁=2, r=3, aₙ=486

Frequently Asked Questions

What is a geometric sequence?

What is the nth term formula?

What if r is negative?

What is r called?

What if |r| < 1?

Related Calculators

Geometric Sequence Calculator

Formula

How It Works

Examples

a₁=2, r=3, n=6

Find r given a₁=2, a₆=486

Find n given a₁=2, r=3, aₙ=486

Frequently Asked Questions

What is a geometric sequence?

What is the nth term formula?

What if r is negative?

What is r called?

What if |r| < 1?

Related Calculators