To find the sum of the given series, we can group the terms in pairs:

(2-4) + (6-8) + ... + (46-48) + 50

Each pair of terms has a difference of -2.

So, the sum of each pair is -2.

Now, we need to find the number of pairs in the series.

The first term is 2 and the last term is 50.

To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

50 = 2 + (n-1)(-2)

50 = 2 - 2n + 2

50 = 4 - 2n

2n = 46

n = 23

Therefore, there are 23 pairs in the series.

Now, we can find the sum of the series by multiplying the number of pairs by the sum of each pair:

Sum = number of pairs * sum of each pair
= 23 * (-2)
= -46

Therefore, the sum of the series 2-4+6-8+...+46-48+50 is -46.