Sequences & Series Visualizer
Compare arithmetic and geometric sequences. Watch terms grow as bars and track partial sums and convergence behavior.
Sequence Parameters
Properties
| Type | -- |
| Formula | -- |
| nth term | -- |
| Sum Sₙ | -- |
| Convergence | -- |
| First terms | -- |
The Math Behind It
Arithmetic Sequences
- nth term: aₙ = a₁ + (n-1)d
- Sum: Sₙ = n(a₁ + aₙ) / 2
- Constant common difference d between terms
- Always diverges unless d = 0
- Graph of terms is a straight line
Geometric Sequences
- nth term: aₙ = a₁ · rn-1
- Sum: Sₙ = a₁(1 - rn) / (1 - r), r ≠ 1
- Constant common ratio r between terms
- Converges if |r| < 1: S∞ = a₁ / (1 - r)
- Diverges if |r| ≥ 1
- |r| < 1: terms shrink toward zero
You're crushing it!