# Geometric Sequence Calculator

Geometric Sequence Calculator helps to compute the first five terms in a geometric sequence. A geometric sequence can also be called a geometric progression. Geometric progressions can be finite or infinite.

## What is Geometric Sequence Calculator?

Geometric Sequence Calculator is an online tool that helps to calculate the first five terms in a geometric sequence when the first term and the common ratio are known. A geometric sequence is one where two consecutive terms have a constant ratio. To use the * geometric sequence calculator*, enter the values in the given input boxes.

### Geometric Sequence Calculator

**NOTE:** Enter first tem(a_{1}) upto three digits and common ratio(r) upto two digits only.

## How to Use Geometric Sequence Calculator?

Please follow the steps below to find the first few terms in a geometric sequence using the geometric sequence calculator:

**Step 1:**Go to Cuemath's online geometric sequence calculator.**Step 2:**Enter the values in the given input boxes.**Step 3:**Click on the**"Calculate"**button to find the terms of the geometric sequence.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Geometric Sequence Calculator Work?

A geometric progression (GP) in which the last term is defined is known as a finite GP. If the last term of a GP is not defined it is known as an infinite GP. If the first term of a GP is given by "a", and the common ratio between two successive terms is given by r, then the GP is given as follows:

Finite GP = a , ar, ar^{2}, ar^{3},.... ,ar^{n - 1}

Infinite GP = a , ar, ar^{2}, ar^{3},....,ar^{n - 1},.....

Here, ar^{n-1} denotes the n^{th} term of a GP. Given below are the steps to find the terms of a GP.

- Keep the first term, a, as it is.
- Multiply a by the common ratio r to get the second term; a × r.
- Multiply the second term by the common ratio to get the third term; ar × r = ar
^{2} - Similarly, keep multiplying the common ratio with the previous term in order to determine the required number of terms.
- You can also substitute the value of n in ar
^{n-1 }to find the various terms in a GP.

## Solved Examples on Geometric Sequence Calculator

**Example 1:**

Find the geometric sequence up to 5 terms if first term(a) = 6, and common ratio(r) = 2. Verify it using the online geometric sequence calculator.

**Solution:**

Given: a = 6, r = 2

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

a_{1}(first term) = 6 × 2^{1 - 1}= 6

a_{2}(second term) = 6 × 2^{2}^{ - 1}= 12

a_{3}(third term) = 6 × 2^{3}^{ - 1}= 24

a_{4}(fourth term) = 6 × 2^{4}^{ - 1}= 48

a_{5}(fifth term) = 6 × 2^{5}^{ - 1}= 96

Therefore, the geometric sequence is {6, 12, 24, 48, 96, ...}

**Example 2:**

Find the geometric sequence up to 5 terms if first term(a) = 125, and common ratio(r) = 1/4. Verify it using the online geometric sequence calculator.

**Solution:**

Given: a = 125, r = 1/4 = 0.25

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

a_{1}(first term) = 125 × 0.25^{1 - 1}= 125

a_{2}(second term) = 125 × 0.25^{2 - 1}= 31.25

a_{3}(third term) = 125 × 0.25^{3 - 1}= 7.81

a_{4}(fourth term) = 125 × 0.25^{4 - 1}= 1.95

a_{5}(fifth term) = 125 × 0.25^{5 - 1}= 0.49

Therefore, the geometric sequence is {125, 31.25, 7.81, 1.95, 0.49, ...}

Similarly, you can try the geometric sequence calculator to find the terms of the geometric sequence for the following:

- First term(a) = 1, common ratio(r) = 1/2
- First term(a) = 5, common ratio(r) = 5

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