Marinada '25

[lang=hr] Sada su potrebna još dva bomba zadatka, a prvi od tih je: Niz $a_n$ zadan je rekurzivno sa \[ a_0=-1 \] \[ a_n=\frac{2a_{n-1}-3}{3a_{n-1}-4}, \quad n\in \mathbb{N} \] Odredi $a_{100}$ (rješenje zapiši u oliku $\frac{a}{b}$ gdje su $a$ i $b$ relativno prosti cijeli brojevi. Kao odgovor na ovo pitanje napiši $a+b$) [/lang] [lang=en] Now two more “bomb” problems are required, and the first of them is: The sequence \(a_n\) is defined recursively by \[ a_0=-1 \] \[ a_n=\frac{2a_{n-1}-3}{3a_{n-1}-4}, \quad n\in \mathbb{N} \] Find $a_{100}$. (Write the solution in the form $\frac{a}{b}$ where $a$ and $b$ are relatively prime integers. As the answer to this question, submit $a+b$.) [/lang]