Example 1: There is an electronic flea jumping back and forth on a number line, and it lights up a red light when it jumps to a negative number, but does not light up when it jumps to a positive number. The starting point is at the point representing the number -2 (record one red light), the first step is to jump 1 unit to the left, the second step is to jump 2 units to the right, the third step is to jump 3 units to the left, the fourth step is to jump 4 units to the right, and so on.
(1) When it jumps to the tenth step, how far is the electronic flea from the origin? How many times has the red light been lit?
(2) If the electronic flea needs to light up the red light ten times, what is the minimum number of jumps it needs to make? At this point, how far is it from the origin?
(1) Notice
$$
\begin{array}{l}
S=\mid-2-1+2-3+4-5+\cdots-9+101 \\
=1-2+1 \times 5 \mid=3 .
\end{array}
$$

Therefore, the negative numbers appear as $-2,-3,-1,-4,-5$, $-6,-7$, a total of seven times. So, the red light will flash seven times.
(2) In fact, after the electronic flea jumps four times, it returns to the origin, and the red light has already flashed four times (including the initial jump). After that, the red light flashes once for each odd-numbered jump. Therefore, to make the red light flash ten times, the electronic flea needs to jump $4+$ $2 \times 6-1=15$ times. At this point, the distance of the electronic flea from the origin is
$$
\begin{array}{l}
S=|-2-1+2-3+4-5+\cdots-15| \\
=|-2+1 \times 7-15|=10 .
\end{array}
$$