To find the sum of the given arithmetic series, we need to find the number of terms and then use the formula for the sum of an arithmetic series.

The first term, a, is -1.
The common difference, d, is -2.
The last term, l, is -201.

We can find the number of terms, n, using the formula:
l = a + (n-1)d

Substituting the given values:
-201 = -1 + (n-1)(-2)

Simplifying:
-201 = -1 - 2n + 2
-201 = 1 - 2n

Rearranging the equation:
2n = 1 + 201
2n = 202
n = 202/2
n = 101

So, there are 101 terms in the series.

Now, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(a + l)

Substituting the given values:
Sn = (101/2)(-1 + (-201))

Simplifying:
Sn = (101/2)(-1 - 201)
Sn = (101/2)(-202)
Sn = -101(202)
Sn = -20,402

Therefore, the sum of the series (-1) + (-3) + (-5) + ... + (-201) is -20,402.