This geometric sequence calculator can help you find a specific number within a geometric progression and all the other figures if you know the scale number, common ratio and which nth number to obtain. You can discover more about the geometric series below the tool.

## How does this geometric sequence calculator work?

In mathematics, a geometric progression is also known as **geometric sequence** and represents a sequence of numbers (sequence being an ordered list of numbers) with the particularity that each member/term excepting the first one is found by multiplying the previous one by a fixed, non-zero number generally called the common ratio.

For example, the sequence 2, 10, 50, 250, 1250, 6250, 31250, 156250, 781250 is a geometric progression with the common ratio being 5.

The formulas applied by this geometric sequence calculator are detailed below while the following conventions are assumed:

- the first number of the geometric progression is a;

- the step/common ratio is r;

- the nth term to be found in the sequence is a_{n};

- The sum of the geometric progression is S.

**Then:**

a_{n }= ar^{n-1}

If r ≠ 1 then S = [a(1-r^{n}]/(1-r)

If r = 1 then S = an

## Example of a geometric progression calculation

Let’s take an example of a geometric progression having first number a= 2, r = 3 for which we try to figure out which is the 10^{th} number in the sequence:

■ The 10^{th} value of the sequence (a_{10}) is 39,366

■ Sample of the first ten numbers in the geometric sequence: 2; 6; 18; 54; 162; 486; 1,458; 4,374; 13,122; 39,366

■ Sum of all numbers until the 10^{th}: 59,048