Geometric Sequence Calculator

A geometric sequence is a sequence where every term bears a constant ratio to its preceding term.

What is Geometric Sequence Calculator?

'Cuemath's Geometric Sequence Calculator' is an online tool that helps to calculate the geometric sequence. Cuemath's online Geometric Sequence Calculator helps you to calculate the geometric sequence in a few seconds.

NOTE: Please enter the values up to two digits only.

How to Use Geometric Sequence Calculator?

Please follow the steps below to find the geometric sequence:

• Step 1: Enter the first term(a), the common ratio(r) in the given input box.
• Step 2: Click on the "Calculate" button to find the geometric sequence.
• Step 3: Click on the "Reset" button to clear the fields and find the geometric sequence for different values.

How to Find Geometric Sequence Calculator?

The general form of an geometric sequence can be written as: 

 Where 'a_n' is the nth term in the sequence, 'a' is the first term, 'r' is the common ratio between two numbers, and 'n' is the nth term to be obtained.

Solved Example:

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

Solution:

Given: a = 6, d = 2

a_n = ar^{n - 1}

a₁(first term) = 6 × 2^{1 - 1}= 6

a₂(second term) = 6 × 2^{2 - 1}= 6 × 2 = 12

a₃(third term) = 6 × 2^{3 - 1}= 6 × 4 = 24

a₄(fourth term) = 6 × 2^{4 - 1}= 6 × 8 = 48

a₅(fifth term) = 6 × 2^{5 - 1}= 6 × 16 = 96

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

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

• First term(a) = 5, common ratio(r) = 10
• First term(a) = 4, common ratio(r) = 5