**Related Pages**

Number Sequences

Linear Sequences

Quadratic and Cubic Sequences

In these lessons, we will look at geometric sequences and how to find the nth term of a geometric sequence.

The following figure gives the formula for the nth term of a geometric sequence. Scroll down the page for examples and solutions on how to use the formula.

The formula for a geometric sequence is

a_{n} = a_{1}r^{n - 1} where a_{1} is the first term and r is
the common ratio.

This video looks at identifying geometric sequences as well as finding the nth term of a geometric sequence.

**Example:**

- Given a
_{1}= 5, r = 2, what is the 6th term? - Given a
_{1}= 11, r = -3, what is a_{8}?

This video shows how derive the formula to find the ’n-th’ term of a geometric sequence by considering an example. The formula is then used to find another term of the sequence.

How to find any term of a geometric sequence?

**Example:**

5, 10, 20, 40, …

This video explains how to find the formula for the nth term of a given geometric sequence given three terms of the sequence.

**Example:**

Given the information about the geometric sequence, determine the formula for the nth term.

a_{0} = 5, a_{1} = 40/9, a_{3} = 320/81, …

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

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