# Geometric Sequences - nth Term

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. ### What Is The Formula For A Geometric Sequence?

The formula for a geometric sequence is
an = a1rn - 1 where a1 is the first term and r is the common ratio.

#### Geometric Sequences

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

Example:

1. Given a1 = 5, r = 2, what is the 6th term?
2. Given a1 = 11, r = -3, what is a8?

#### Geometric Sequences: A Formula For The nth Term.

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.

#### Finding The nth Term Of A Geometric Sequence

How to find any term of a geometric sequence?

Example:
5, 10, 20, 40, …

#### Find The Formula For A Geometric Sequence Given Terms

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.
a0 = 5, a1 = 40/9, a3 = 320/81, …

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