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If x 1 , x 2 , … . . , x n and 1 h 1 , 1 h 2 , … . . , 1 h n are two A.P.s such that x 3 = h 2 = 8 & x 8 = h 7 = 20 , then x 5 · h 10 is equal to

Options

  1. A3200
  2. B1600
  3. C2650
  4. D2560

Correct answer

D. 2560

Step-by-step solution

Let d 1 be the common difference of the A.P. x 1 , x 2 , … , then x 8 - x 3 = 5   d 1 = 12 ⇒ ⇒ x 5 = x 3 + 2   d 1 = 8 + 2 × 12 5 = 12 . 8 Let d 2 be the common difference of the other sequence then 5   d 2 = 1 20 - 1 8 = - 3 40 ⇒ d 2 ⇒ 1   h 10 = 1   h 7 + 3   d 2 = 1 200 ⇒ h 10 = 200 ⇒ x 5 · h 10 = 12 . 8 × 200 = 2560

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