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Let a 1 , a 2 , a 3 be three positive numbers which are in geometric progression with common ratio r . The inequality a 3 > a 2 + 2 a 1 holds true if r is equal to

Options

  1. A2
  2. B1.5
  3. C0.5
  4. D2.5

Correct answer

D. 2.5

Step-by-step solution

a 2 = a 1 r , a 3 = a 1 r 2 a 3 > a 2 + 2 a 1 ⇒ a 1 r 2 > a 1 r + 2 a 1 ⇒ r 2 - r - 2 > 0 ⇒ r - 2 r + 1 > 0 ⇒ r < - 1 or r > 2

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