The sequence given is an arithmetic sequence with alternating positive and negative terms:

\( (99 - 97) + (95 - 93) + \ldots + (3 - 1) \).

Each pair, like \(99 - 97\) and \(95 - 93\), simplifies to:

\[ 99 - 97 = 2, \]
\[ 95 - 93 = 2, \]
\[ \ldots \]
\[ 3 - 1 = 2. \]

There are pairs starting from 99 and ending at 3. To find the number of pairs, observe:

- The sequence of numbers being paired is \(99, 97, 95, \ldots, 3\).
- This sequence is an arithmetic sequence with a common difference of \(-2\).

The nth term of this sequence can be found using the formula:
\[ a_n = a_1 + (n-1)d \]

Where \(a_1 = 99\) and \(d = -2\). We want the term that equals 3:

\[ 3 = 99 + (n-1)(-2) \]
\[ 3 = 99 - 2n + 2 \]
\[ 3 = 101 - 2n \]
\[ 2n = 101 - 3 \]
\[ 2n = 98 \]
\[ n = 49 \]

So, there are 49/2 = 24.5 pairs, meaning there are 24 pairs and a single unpaired 1 at the end. Therefore:

Sum of all pairs \(= 24 \times 2 = 48.\)

Since it ends with \(-1\), subtract 1:
Total sum = \(48 - 1 = 47.\)

Thus, the final result is \(47\).