Recursive Sequence

Direct substitution in the recurrence relation $\large f_n =\frac{f_{n-1} +1}{f_{n-2}} ,\ \ n =0,1,2,\cdots$ gives the following :-

$\begin{aligned} \color{#D61F06} f_0&=24.8 \\ f_1&=36.9 \\ f_2&=1.52823 \\ f_3&=0.0685156\\ f_4&=0.699187\\ \color{#D61F06}f_5&=24.8\\ f_6&=36.9\\ f_7&=1.52823\\ f_8&=0.0685156\\ f_9&=0.699187\\ \color{#D61F06}f_{10}&=24.8\\ f_{11}&=36.9\\ f_{12}&=1.52823\\ f_{13}&=0.0685156\\ f_{14}&=0.699187\\ \color{#D61F06}f_{15}&=24.8\\ \cdots&=\cdots\\ \end{aligned}$

The above sequence has cycle with length $= 5$

$f_{4445} = f_{4445 \% 5} = f_0 = 24.8$

Answer $= 10 \times 24.8 = 248$