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.