Series Calculator

Result

Your result will appear here...

How to use:

  • Select the series type (Arithmetic, Geometric, or Infinite Geometric)
  • Enter the first term (a₁)
  • Enter the common difference (d) for arithmetic or common ratio (r) for geometric series
  • For finite series, enter the number of terms (n)
  • Click "Calculate Sum" to see the result
  • Use "Show Example" to load sample values

Formulas:

  • Arithmetic Series: Sₙ = n/2 × (2a₁ + (n-1)d)
  • Finite Geometric Series: Sₙ = a₁(1 - rⁿ)/(1 - r) when r ≠ 1
  • Infinite Geometric Series: S = a₁/(1 - r) when |r| < 1

Examples:

  • Arithmetic: 2 + 5 + 8 + 11 (n=4, a₁=2, d=3) → Sum = 26
  • Geometric: 3 + 6 + 12 + 24 (n=4, a₁=3, r=2) → Sum = 45
  • Infinite Geometric: 1 + 0.5 + 0.25 + ... (a₁=1, r=0.5) → Sum = 2