The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If r \neq 1 is the common ratio, then what is the number of possible <strong>REAL</strong> values of r?
- A. One
- B. Two ✓
- C. Three
- D. More than three
Correct Answer: B. Two
Explanation
S_8 = 5 S_4 \implies a(r^8-1)/(r-1) = 5a(r^4-1)/(r-1). Let x = r^4. x^2 - 1 = 5(x - 1) \implies x = 4 (since r \neq 1). r^4 = 4 \implies r^2 = 2 \implies r = \pm\sqrt{2}. Two real values.
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