Answer:
[tex]t(n)=12 \cdot 3^{n-1}[/tex]
Step-by-step explanation:
From inspection, the points on the graph are:
Therefore, as terms of a sequence:
[tex]t_1=12\\\\t_2=36\\\\t_3=108[/tex]
The difference between the y-coordinates is not equal, therefore the sequence is geometric.
Geometric sequence formula: [tex]t_n=t_1r^{n-1}[/tex]
As [tex]t_1=12 \implies t_n=12r^{n-1}[/tex]
To find r, divide one term by the previous term:
[tex]r=\dfrac{t_3}{t_2}=\dfrac{108}{36}=3[/tex]
Therefore, geometric sequence formula: [tex]t_n=12 \cdot 3^{n-1}[/tex]
