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JEE Main201911 Jan 2019Morning ShiftMathematicsSequences and SeriesActual

Let a₁, a₂, , a₁₀ be a G.P. If a₃ a₁ =25, then a₉ a₅ equals :

Options

  1. A5⁴
  2. B4 (5² )
  3. C5³
  4. D2 (5² )

Correct answer

A. 5⁴

Step-by-step solution

Let a₁=a, a₂=a r, a₃=a r² a₁₀=a r⁹ where r= common ratio of given G.P. Given, a₃ a₁ =25 a r² a =25 r= 5 Now, a₉ a₅ = a r⁸ a r⁴ =r⁴=( 5)⁴=5⁴

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