Geometric Series Calculator 8 2 N 5 N

A geometric series is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. This calculator helps you calculate the sum of a finite geometric series with given parameters.

What is a Geometric Series?

A geometric series is a series where each term after the first is found by multiplying the previous term by a constant called the common ratio (r). The series can be written as:

a + ar + ar² + ar³ + ... + ar^(n-1)

Where:

a is the first term
r is the common ratio
n is the number of terms

The sum of the first n terms of a geometric series is called the geometric series sum.

Formula

The sum S of the first n terms of a geometric series is given by:

S = a(1 - rⁿ) / (1 - r) when r ≠ 1

S = a × n when r = 1

Where:

S is the sum of the series
a is the first term
r is the common ratio
n is the number of terms

Note: The formula only applies when the common ratio r is not equal to 1. If r = 1, the series becomes an arithmetic series with common difference 0.

How to Use This Calculator

Enter the first term (a) of the geometric series
Enter the common ratio (r) between terms
Enter the number of terms (n) you want to sum
Click "Calculate" to compute the sum
View the result and the series terms chart

The calculator will display the sum of the series and show a chart of the series terms.

Example Calculation

Let's calculate the sum of a geometric series with:

First term (a) = 8
Common ratio (r) = 2
Number of terms (n) = 5

The series is: 8, 16, 32, 64, 128

Using the formula:

S = 8(1 - 2⁵) / (1 - 2) = 8(1 - 32) / (-1) = 8(-31) / (-1) = 248 / 1 = 248

The sum of the series is 248.

Term Number	Term Value
1	8
2	16
3	32
4	64
5	128

FAQ

What is a geometric series?: A geometric series is a series where each term after the first is found by multiplying the previous term by a constant called the common ratio.
When is the geometric series formula valid?: The formula is valid when the common ratio r is not equal to 1. If r = 1, the series becomes an arithmetic series with common difference 0.
Can I calculate the sum of an infinite geometric series with this calculator?: No, this calculator is designed for finite geometric series only. For infinite series, the sum formula is S = a / (1 - r) when |r| < 1.
What if the common ratio is negative?: The calculator will work with negative common ratios. The sign of the terms will alternate based on the value of r.
How accurate are the calculations?: The calculator uses standard floating-point arithmetic, which provides accurate results for most practical purposes.