Geometric Sequence Calculator — Formule
## 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.
### 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.
Exemple Résolu
Geometric sequence: first term = 2, common ratio = 3, 6 terms.
- a₆ = 2 × 3⁵ = 2 × 243 = 486
- Sum = 2 × (1 - 3⁶) / (1 - 3) = 2 × (1 - 729) / (-2) = 728
- Sequence: 2, 6, 18, 54, 162, 486