bac-s-maths 2023 Q3

bac-s-maths · France · bac-spe-maths__metropole-sept_j1 1 marks Sequences and series, recurrence and convergence Multiple-choice on sequence properties
For questions 3. and 4., consider the sequence $(u_n)$ defined on $\mathbb{N}$ by: $$u_0 = 15 \text{ and for every natural number } n : u_{n+1} = 1{,}2\, u_n + 12.$$
The following Python function, whose line 4 is incomplete, must return the smallest value of the integer $n$ such that $u_n > 10000$. \begin{verbatim} def seuil() : n=0 u=15 while ......: n=n+1 u=1,2*u+12 return(n) \end{verbatim} On line 4, we complete with: a. $\mathrm{u} \leqslant 10000$; b. $\mathrm{u} = 10000$ c. $\mathrm{u} > 10000$; d. $n \leqslant 10000$.
For questions 3. and 4., consider the sequence $(u_n)$ defined on $\mathbb{N}$ by:
$$u_0 = 15 \text{ and for every natural number } n : u_{n+1} = 1{,}2\, u_n + 12.$$

The following Python function, whose line 4 is incomplete, must return the smallest value of the integer $n$ such that $u_n > 10000$.
\begin{verbatim}
def seuil() :
    n=0
    u=15
    while ......:
        n=n+1
        u=1,2*u+12
    return(n)
\end{verbatim}
On line 4, we complete with:\\
a. $\mathrm{u} \leqslant 10000$;\\
b. $\mathrm{u} = 10000$\\
c. $\mathrm{u} > 10000$;\\
d. $n \leqslant 10000$.