Answer:
[tex]T_{12} = 354294 + 354294i[/tex]
Step-by-step explanation:
Given
Geometric Sequence (GP)
[tex]T_1 = 2 + 2i[/tex]
[tex]r = 3[/tex]
Required
Determine T₁₂
The nth term of a GP is calculated as thus;
[tex]T_n = ar^{n-1}[/tex]
In this case;
[tex]n = 12[/tex]; [tex]r = 3[/tex] and [tex]a = T_1 = 2 + 2i[/tex]
Substitute these values in the above formula
[tex]T_{12} = (2 + 2i) * 3^{12-1}[/tex]
[tex]T_{12} = (2 + 2i) * 3^{11}[/tex]
[tex]T_{12} = (2 + 2i) * 177147[/tex]
Open the bracket
[tex]T_{12} = 177147 * 2 + 177147 * 2i[/tex]
[tex]T_{12} = 354294 + 354294i[/tex]
Hence, the 12th term of the sequence is [tex]T_{12} = 354294 + 354294i[/tex]
