Question

given the sequence tn defined recursively below, find t4.

Answer 1

Answer:

$t_4 = 20$

Step-by-step explanation:

The base case in the recursive function are:

$t_1 = 1$

$t_2 = 2$

The recursive case is equal to:

$t_n = 2t_{n-1} + 3t_{n-2}$

So replace $t_n$ for $t_4$:

$t_4 = 2t_{3} + 3t_{2}$

In the new expression $t_2$ is a base case so you don't have to worry for that part, but $t_3$ is still the recursive case so evaluate again in $t_n$

$t_3 = 2t_{2} + 3t_{1}$

$t_2$ and $t_1$ are define as base cases so you replace for it's numbers:

$t_3 = 2(2) + 3(1) = 7$

Now return to $t_4$ and replace for the new values:

$t_4 = 2(7) + 3(2) = 14 + 6 = 20$

So the final answer is 20