Find the sum of the infinite geometric series: 12 - 4 + 4/3 - 4/9 + ...
Answer and explanation
Correct answer: B. 9
- Step 1: Identify the first term a_1 = 12.
- Step 2: Identify the common ratio r = -4 / 12 = -1/3.
- Step 3: Since |r| < 1, the sum to infinity is S = a_1 / (1 - r).
- Step 4: S = 12 / (1 - (-1/3)) = 12 / (4/3) = 12 * 3 / 4 = 9.
Answer
9.
Why not the others: 8 evaluates 12 / (1 + 1/2); 18 computes 12 / (1 - 1/3) using r = 1/3 without the negative sign; 6 evaluates 12 / 2.
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