If the sum of an infinite geometric series with first term a = 12 is 36, what is the common ratio r?
Answer and explanation
Correct answer: A. r = 2/3
- Step 1: Use infinite geometric series sum formula S = a / (1 - r). Step 2. Substitute values: 36 = 12 / (1 - r). Step 3. Multiply by (1 - r): 36(1 - r) = 12 => 1 - r = 12/36 = 1/3. Step 4. Solve for r: r = 1 - 1/3 = 2/3. Answer: r = 2/3. Why not the others: r = 1/3 is the value of 1 - r, not r; 1/2 and 3/4 yield sums of 24 and 48.
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