Since
[tex]a_i=3a_{i-1}[/tex]then the rate of this geometric series is 3, so we can rewrite the equation in the following form:
[tex]a_{i\text{ }}=3^{i-1}\cdot a_{1\text{ }}=3^{i-1}\cdot2[/tex]Using this expression we calculate the third term of the series,
[tex]a_3=3^{3-1}\cdot2\text{ = 9}\cdot2\text{ =18}[/tex]