Final answer:
The sum of the infinite geometric series -12, -4, 4/3, -4/9 is found using the formula for the sum of an infinite geometric series, resulting in -18.
Step-by-step explanation:
The objective is to find the sum of the infinite geometric series: -12, -4, 4/3, -4/9. To find the sum of an infinite geometric series, the formula S = a / (1 - r) is used where a is the first term and r is the common ratio.
First, we need to determine the common ratio (r) by dividing the second term by the first term: r = (-4) / (-12) = 1/3. Then, apply the formula using the first term a = -12 and the common ratio r = 1/3.
The sum S is then calculated as follows: S = (-12) / (1 - (1/3)) = -12 / (2/3) = -12 * (3/2) = -18.
Thus, the sum of the series is -18, which corresponds to option (a).