Answer:
[tex]t_4 = 20[/tex]
Step-by-step explanation:
The base case in the recursive function are:
[tex]t_1 = 1[/tex]
[tex]t_2 = 2[/tex]
The recursive case is equal to:
[tex]t_n = 2t_{n-1} + 3t_{n-2}[/tex]
So replace [tex]t_n[/tex] for [tex]t_4[/tex]:
[tex]t_4 = 2t_{3} + 3t_{2}[/tex]
In the new expression [tex]t_2[/tex] is a base case so you don't have to worry for that part, but [tex]t_3[/tex] is still the recursive case so evaluate again in [tex]t_n[/tex]
[tex]t_3 = 2t_{2} + 3t_{1}[/tex]
[tex]t_2[/tex] and [tex]t_1\\[/tex] are define as base cases so you replace for it's numbers:
[tex]t_3 = 2(2) + 3(1) = 7[/tex]
Now return to [tex]t_4[/tex] and replace for the new values:
[tex]t_4 = 2(7) + 3(2) = 14 + 6 = 20[/tex]
So the final answer is 20
