Number Sequence Calculator

1. Enter your sequence as comma-separated numbers. Enter at least 3 terms for reliable detection (5 or more is better).
2. The calculator detects the type automatically:
   • Arithmetic: constant difference between terms (e.g., 3, 7, 11, 15)
   • Geometric: constant ratio between terms (e.g., 2, 6, 18, 54)
   • Fibonacci-like: each term is the sum of the two before it
3. Read the next 5 predicted terms, the nth term formula, and other properties.

Use the preset buttons to explore common sequences quickly.

Arithmetic Sequence:
  a(n) = a1 + (n - 1) × d
  Where a1 = first term, d = common difference
  Example: 3, 7, 11, 15... a1=3, d=4
  a(n) = 3 + (n-1) × 4 = 4n - 1
  Sum of first n terms: Sn = n/2 × (2a1 + (n-1)d)

Geometric Sequence:
  a(n) = a1 × r^(n-1)
  Where a1 = first term, r = common ratio
  Example: 2, 6, 18, 54... a1=2, r=3
  a(n) = 2 × 3^(n-1)
  Sum of first n terms (r ≠ 1): Sn = a1 × (1-r^n) / (1-r)

Fibonacci Sequence:
  F(1) = 1, F(2) = 1
  F(n) = F(n-1) + F(n-2) for n > 2
  1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
  Closed form (Binet's formula):
  F(n) = [φ^n - ψ^n] / √5
  Where φ = (1+√5)/2 ≈ 1.618 (golden ratio), ψ = (1-√5)/2