# Geometric sequences

### 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.