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Let a 1 , a 2 , a 3 , … , be a G . P . such that a 1 < 0 , a 1 + a 2 = 4 and a 3 + a 4 = 16 . If ∑ i = 1 9 a i = 4 λ , then λ , is equal to.

Options

  1. A- 513
  2. B- 171
  3. C171
  4. D511 3

Correct answer

B. - 171

Step-by-step solution

a 1 + a 2 = 4 ⇒ a 1 + a 1 r = 4 … 1 a 3 + a 4 = 16 ⇒ a 1 r 2 + a 1 r 3 = 16 … 2 1 r 2 = 1 4 ⇒ r 2 = 4   ⇒ r = - 2     a 1 < 0 ∑ i = 1 a a i = a 1 r 9 - 1 r - 1 = - 4 - 2 9 - 1 - 2 - 1 = 4 3 - 513 = 4 λ λ = - 171 .

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