Arithmetic & Geometric Series Calculator

Learn how to calculate the sum of arithmetic and geometric series. Enter the first term, common difference or ratio, and number of terms. The calculator will show formulas and step-by-step calculations.

Series Type: --Select-- Arithmetic Geometric

First term (a):

Common difference (d) / ratio (r):

Number of terms (n):

Calculate Sum

About Series

An arithmetic series is a sequence of numbers with a constant difference between consecutive terms. The sum formula is S_n = n/2 × (2a + (n-1)d).

A geometric series is a sequence where each term is multiplied by a constant ratio. The sum formula is S_n = a × (1 - r^n) / (1 - r) (if r ≠ 1).

• Arithmetic example: 2, 5, 8, 11 → d = 3
• Geometric example: 3, 6, 12, 24 → r = 2

Use this calculator for homework, learning, or understanding series concepts step-by-step.