Explore Series Sums with Ease

Calculate sums of Arithmetic and Geometric series using our interactive calculator. Visualize formulas and get instant results.

Calculate Series Sum

Series Type

First Term (a)

Common Difference (d)

Common Ratio (r)

Number of Terms (n)

Understanding Series Sums

In mathematics, a series is the sum of the terms of a sequence. This tool focuses on two common types of series: Arithmetic and Geometric.

Arithmetic Series

An arithmetic series is a sequence of numbers such that the difference between the consecutive terms is constant. This constant difference is called the common difference, denoted as 'd'. The sum of the first 'n' terms of an arithmetic series is given by the formula:

$$S_n = \frac{n}{2} [2a + (n-1)d]$$

Where 'a' is the first term and 'n' is the number of terms.

Geometric Series

A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio, denoted as 'r'. The sum of the first 'n' terms of a geometric series is given by:

$$S_n = \frac{a(1 - r^n)}{1 - r}$$

Where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms. For r = 1, the sum is simply S_n = n × a.

Use this calculator to quickly compute the sum of series by entering the first term, common difference or ratio, and the number of terms.