Geometric sequences

Lesson: 1a
3:39
Lesson: 1b
7:02
Lesson: 1c
4:35
Lesson: 2
6:59
Lesson: 3
9:57

Learn
Practice

Geometric sequences

A geometric sequence, also called geometric progression, is a number sequence with a common ratio between successive terms. A term in a geometric sequence can be found by multiplying the previous one by a non-zero and fixed number (a common ratio).

Basic Concepts: Arithmetic sequences

Lessons

• geometric sequence: a sequence with a common ratio between successive terms.
• the nth term,

{t_n}

,of a geometric sequence:

{t_n}\; = \;{t_1} \cdot {r^{n - 1}}

where,

{t_n}

: nth term

{t_1}

: first term
r : common ratio

1.
Geometric sequence formula
Consider the geometric sequence: 2, 6, 18, 54, … .
a)
Identify the common ratio.

b)
Determine the sixth term of the sequence.

c)
Which term in the sequence has a value of 39366?

2.
Determine $t_1,r,t_n$ for the sequences in which two terms are given:
$t_3=18$ , $t_6=486$

3.
Three consecutive terms of a geometric sequence are written in the form
$5(x+2),8-x,x-2$
Find the common ratio and the possible value of each of the three terms.

Geometric sequences

Geometric sequences

Lessons

Do better in math today

Don't just watch, practice makes perfect

Practice topics for Sequences and Series