Number Sequence Calculator

Generate sequences, find patterns, calculate nth terms, and compute sums for various number sequences

Sequence Calculator

Choose sequence type and calculation mode

About Number Sequences

Arithmetic Sequences

  • Pattern: Constant difference between terms
  • Formula: a(n) = a₁ + (n-1)d
  • Sum: S(n) = n/2 × [2a₁ + (n-1)d]

Geometric Sequences

  • Pattern: Constant ratio between terms
  • Formula: a(n) = a₁ × r^(n-1)
  • Sum: S(n) = a₁(r^n - 1)/(r - 1)

Fibonacci Sequence

  • Pattern: Each term = sum of previous two
  • Starts: 0, 1, 1, 2, 3, 5, 8, 13...
  • Golden Ratio: Ratio approaches φ ≈ 1.618

Pattern Recognition

  • Detects arithmetic and geometric patterns
  • Identifies Fibonacci-like sequences
  • Recognizes quadratic sequences
  • Predicts next terms based on pattern