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JEE Main201815 Apr 2018Morning ShiftMathematicsSequences and SeriesActual

If x₁, x₂, ., x_n and 1 h₁ , 1 h^2 , . . 1 h_n are two A.P's such that x₃=h₂=8 and x₈=h₇=20 , then x₅ . h₁₀ equals.

Options

  1. A2560
  2. B2650
  3. C3200
  4. D1600

Correct answer

A. 2560

Step-by-step solution

Suppose d₁ is the common difference of the A.P. x₁, x₂, . x_n then aligned & x₈-x₃=5 d₁=12 d₁= 12 5 =2.4 & x₅=x₃+2 d₁=8+2 12 5 =12.8 aligned Suppose d₂ is the common difference of the A.P 1 h₁ , 1 h₂ , . 1 h_n then aligned &5 d₂= 1 20 - 1 8 = -3 40 d₂= -3 200 & 1 h₁₀ = 1 h₇ +3 d₂= 1 200 h₁₀=200 & x₅ . h₁₀=12.8 200=2560 aligned

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