Answer:
r = - [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The n th term of a GP is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 18 and a₆ = - [tex]\frac{2}{27}[/tex] , then
18 [tex]r^{5}[/tex] = - [tex]\frac{2}{27}[/tex] ( divide both sides by 18 )
[tex]r^{5}[/tex] = - [tex]\frac{1}{243}[/tex] ( take the fifth root of both sides )
r = [tex]\sqrt[5]{-\frac{1}{243} }[/tex] = - [tex]\frac{1}{3}[/tex]
