Geometric Sequences - nth Term

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.

• Printable & Online Sequence Worksheets

  Find the sequence & n^th term
  Find the sequence & n^th term
  Find the n^th term of a sequence with fractions

What Is The Formula For A Geometric Sequence?

The formula for a geometric sequence is
a_n = a₁r^{n - 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?

• Show Video Lesson

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.

• Show Video Lesson

Finding The nth Term Of A Geometric Sequence

How to find any term of a geometric sequence?

Example:
5, 10, 20, 40, …

• Show Video Lesson

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, …

• Show Video Lesson

Check out our most popular games!
Fraction Concoction	Fact Family Game	Number Bond Garden
Online Addition Subtraction Game	Penguin Solitaire	Sawayama Solitaire
Ark Solitaire	Eldritch Invasion	Shenzhen Solitaire

Check out more Solitaire games here.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.