Find the missing term in the sequence: 5824, 5242, ?, 4247, 3823.

The sequence is $5824, 5242, ?, 4247, 3823$.
Let the terms be $T_1, T_2, T_3, T_4, T_5$.
$T_1 = 5824$
$T_2 = 5242$
$T_3 = ?$ (the missing term)
$T_4 = 4247$
$T_5 = 3823$

The difference between $T_1$ and $T_2$:

The difference between $T_4$ and $T_5$:

Observe the relationship between a term $T_n$ and the difference $D_n$ (which is $T_n - T_{n+1}$).
For $T_1 = 5824$, the difference $D_1 = 582$. Notice that 582 is the number formed by the first three digits of 5824. This can be expressed using the floor function: $\lfloor T_1 / 10 \rfloor = \lfloor 5824 / 10 \rfloor = 582$.
So, $T_2 = T_1 - \lfloor T_1 / 10 \rfloor$.

Let's check this pattern for $T_4$:
For $T_4 = 4247$, the difference $D_4 = 424$. Similarly, $\lfloor T_4 / 10 \rfloor = \lfloor 4247 / 10 \rfloor = 424$.
So, $T_5 = T_4 - \lfloor T_4 / 10 \rfloor$.

The established pattern is $T_{n+1} = T_n - \lfloor T_n / 10 \rfloor$.

Using the pattern for $T_2$ to find $T_3$:

Substitute the value of $T_2$:

If $T_3 = 4718$, then $T_4$ should follow the pattern:

This calculated value of $T_4$ matches the given $T_4$ in the sequence, confirming the correctness of the pattern and the missing term.

The missing term is 4718.