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KCET2020MathematicsLimits

If a₁ a₂ a₃ a₉ are in AP , then the value of | array lll a₁ & a₂ & a₃ a₄ & a₅ & a₆ a₇ & a₈ & a₉ array | is

Options

  1. A9 2 (a₁+a₉ )
  2. B(a₁+a₉ )
  3. C_ e ( _ e e )
  4. D1

Correct answer

C. _ e ( _ e e )

Step-by-step solution

a₁, a₂, a₃, , a₉ are in AP. | array lll a₁ & a₂ & a₃ a₄ & a₅ & a₆ a₇ & a₈ & a₉ array | Apply R₁ R₁+R₂-2 R₂ | array ccc a₁+a₇-2 a₄ & a₂+a₈-2 a₅ & a₃+a₉-2 a₆ a₄ & a₅ & a₆ a₇ & a₈ & a₉ array | | array ccc 0 & 0 & 0 a₄ & a₅ & a₆ a₇ & a₈ & a₉ array | aligned & [ a₁+a₇-2 a₄=a₁+a₁+6 d-2 a₁-6 d=0 . & Similarly .a₂+a₄-2 a₅=0, a₃+a₉-2 a₆=0 ] &=0 &= _ e 1= _ e ( _ e e ) aligned

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