If $z^3 + (3 + 2i)z + (-1 + ia) = 0$ has one real root, then the value of $a$ lies in the interval $(a \in \mathbb{R})$
Step-by-Step Solution
Key Concept: The recurrence relation follows from conditioning on the first outcome and the constraint structure.
For the sequence, $a_0 = 2$ with outcomes in $\{H, T\}$. For $a_2 = 3$ with outcomes in $\{HT, TH, TT\}$. For $n \geq 3$, if the first outcome is $H$, then $T$ follows, giving $a_{n-2}$. If the first outcome is $T$, then $a_{n-1}$ follows. Thus $a_n = a_{n-1} + a_{n-2}$, yielding $a_3 = 5, a_4 = 8$.
Correct Answer: 1,2,4