Geometric Sequence Calculator
Find the nth term, sum, and properties of a geometric sequence given the first term, common ratio, and number of terms.
Nth Term
486.0000
Formula
## Geometric Sequence ### nth Term **aₙ = a₁ × r^(n-1)** ### Sum of n Terms **Sₙ = a₁ × (1 - r^n) / (1 - r)** (when r ≠ 1) ### Infinite Sum (converges only when |r| < 1) **S∞ = a₁ / (1 - r)** A geometric sequence has a constant ratio between consecutive terms.
Exemplo Resolvido
Geometric sequence: first term = 2, common ratio = 3, 6 terms.
- 01a₆ = 2 × 3⁵ = 2 × 243 = 486
- 02Sum = 2 × (1 - 3⁶) / (1 - 3) = 2 × (1 - 729) / (-2) = 728
- 03Sequence: 2, 6, 18, 54, 162, 486
Perguntas Frequentes
What is a geometric sequence?
A geometric sequence has a constant ratio between consecutive terms. Examples: 2,6,18,54... (r=3) or 100,50,25,12.5... (r=0.5).
When does the infinite sum converge?
The infinite sum converges only when |r| < 1. When |r| ≥ 1, the terms grow without bound and the sum is infinite.
What is the common ratio?
The common ratio r is the factor you multiply by to get from one term to the next: r = a₂/a₁.
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