Use the formula to evaluate the series 2 - 10 + 50 - 250 + ... a6 sn = a1 (1-r^n) / 1-r

The given is a geometric sequence where the consecutive terms have a common ratio of - 5. The first term is given to be 2 and the number of terms is 6. If we are to substitute the known variables to the equation,

Sn = (2) (1 - (-5) ^6) / (1 - - 5)

The value of Sn from the equation is - 5208. Thus, the sum of the first six terms of the geometric sequence is - 5208.