Geometric Sequence Calculator

Calculate geometric sequence terms and sums. Free online geometric progression calculator.

The Geometric Sequence Calculator finds terms and sums in a geometric progression where each term is multiplied by a constant ratio. Enter the first term and common ratio to generate the sequence, find any term, or calculate partial and infinite sums. Essential for compound interest, population growth, and exponential patterns.

Common use cases

  • Compound interest calculations
  • Population growth modeling
  • Depreciation calculations
  • Fractal patterns
  • Signal attenuation

How to use

  1. Enter the first term (a₁)
  2. Enter the common ratio (r)
  3. Specify terms or sum to calculate
  4. Click calculate for results
  5. View the sequence and sums

FAQ

What is a geometric sequence?

A sequence where each term equals the previous term times a constant (common ratio). Example: 3, 6, 12, 24... (r=2).

What is the nth term formula?

aₙ = a₁ × r^(n-1), where a₁ is first term, r is common ratio, n is term number.

What is the sum formula?

For r≠1: Sₙ = a₁(1-rⁿ)/(1-r). For infinite series with |r|<1: S∞ = a₁/(1-r).

When does infinite sum exist?

Only when |r| < 1. The terms approach zero, allowing the sum to converge to a finite value.