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# Geometric Sequence Calculator

Provide the value of the first term, ratio, and the term you want to find (nth term) to the geometric sequence calculator.

## Geometric Sequence Calculator

The geometric progression calculator finds any value in a sequence. It uses the first term and the ratio of the progression to calculate the answer. You can enter any digit e.g **7**, **100 **e.t.c and it will find that number of value.

This tool gives the answer within a second and you can see all of the steps that are required to solve for the value, yourself.

## What is a sequence?

In general, a **sequence **is a set of integers that go on with a flow. It means that each term is different from its previous value in the same way as the term next to it is from itself. For example:

All of the values in this sequence differ from their previous value by **-2**.

## What is a Geometric sequence?

The Definition of a geometric sequence is:

“Such a sequence in which the difference (**d**) between the two consecutive terms is a ratio (**r**)”

Each new term is found by multiplying the preceding term with this ratio.

## Geometric sequence formula

We use a formula to find any number value in a geometric sequence. This formula is:

**a**_{n} = a_{1 }r^{n-1}

**a**

_{n}= a_{1 }r^{n-1}In this equation;

**a**_{n}is the term we want to find.**a**_{1}is the first term of the sequence.**r**is the ratio.**n**is the number of the number we need.

## How to find the nth value in a geometric sequence?

One way is to use the **geometric sequences calculator**. The second option is manual. To learn how to find the nth term in a geometric progression, see the example ahead.

**Example**

Find the **8th** term for a sequence. The first value of the sequence is **3**. The ratio between the terms is **2/3**.

*Solution:*

**Step 1:** Identify the values.

a_{1} = 3

r = 2/3

n = 8th

**Step 2:** Use the values in the formula.

`a`

_{n} = a_{1}r^{n-1}

a_{8} = (3)(⅔)^{8-1}

a_{8} = (3)(⅔)^{7}

a_{8} = (3)(0.000914)

`a`

_{8} = **0.0027**