# Geometric sequences

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##### Examples
###### Lessons
1. Geometric sequence formula
Consider the geometric sequence: 2, 6, 18, 54, … .
1. Identify the common ratio.
2. Determine the sixth term of the sequence.
3. 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:
$t_3=18$, $t_6=486$
1. 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.
###### Topic Notes
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).
• 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