What is the sum of the first six terms of the geometric series?

2 – 6 + 18 – 54 +

-486
–364
–40
122

This may be done manually by identifying the next two terms of the sequence. To do so, identify first the common ratio of the geometric sequence. 
 
                                     common ratio, r = (-6 / 2) = -3

The next two terms are 
                                           a5 = (-54)(-3) = 162
                                           a6 = (162)(-3) = -486

Solve for the sum of the first six terms
 
                                 S = 2 -6 +18 -54 +162 -486 = -364

Thus, the answer is -364 which is the second among the choices. 

Step 1: 6x-10=1; step 2: 6x=11