Answer:
[tex]r = 6[/tex]
Step-by-step explanation:
Given
[tex]a = 3[/tex] --- First, term
[tex]T_4 = 648[/tex] --- Fourth term
Required: Determine the common ratio
The nth term of a GP is
[tex]T_n = ar^{n-1[/tex]
Substitute 4 for n
[tex]T_4 = ar^{4-1[/tex]
[tex]T_4 = ar^{3[/tex]
Substitute 648 and 3 for T4 and 3 respectively.
[tex]648 = 3 * r^{3[/tex]
[tex]r^3 = 216[/tex]
Take cube roots of both sides
[tex]r =\sqrt[3]{216}[/tex]
[tex]r = 6[/tex]
The common ratio is 6
