Identify, extend, and analyse arithmetic, geometric, Fibonacci, and other number sequences. Find the nth term and partial sums.
Enter the known terms of your sequence (at least 3), separated by commas.
Generate a sequence
| Property | Value |
|---|
| n | Term (aₙ) | Partial Sum (Sₙ) |
|---|
| Type | Definition | Formula | Example |
|---|---|---|---|
| Arithmetic | Constant difference (d) | aₙ = a₁ + (n−1)d | 2, 5, 8, 11, … |
| Geometric | Constant ratio (r) | aₙ = a₁ × rⁿ⁻¹ | 2, 6, 18, 54, … |
| Fibonacci | Each term = sum of previous two | aₙ = aₙ₋₁ + aₙ₋₂ | 1, 1, 2, 3, 5, 8, … |
| Triangular | Count of dots in triangle | aₙ = n(n+1)/2 | 1, 3, 6, 10, 15, … |
| Square | Perfect squares | aₙ = n² | 1, 4, 9, 16, 25, … |
Arithmetic series: Sₙ = n/2 × (a₁ + aₙ) = n/2 × (2a₁ + (n−1)d)
Geometric series (r≠1): Sₙ = a₁ × (1−rⁿ)/(1−r)
Infinite geometric series (|r|<1): S∞ = a₁/(1−r)