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Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series

The m ^ th term of an arithmetic progression is x and the n ^ th term is y . Then the sum of the first (m+n) terms is

Options

  1. Am+n 2 [(x+y)+ x-y m-n ]
  2. Bm+n 2 [(x-y)+ x+y m-n ]
  3. C1 2 [ x+y m+n + x-y m-n ]
  4. D1 2 [ x+y m+n - x-y m-n ]

Correct answer

A. m+n 2 [(x+y)+ x-y m-n ]

Step-by-step solution

Let first term is a then x=a+(m-1) d, y=a+(n-1) d and s= m+n 2 [2 a+(m+n-1) d](x+y)=2 a+(m+n-2) d and (x-y)=(m-n) d aligned & d= ( x-y m-n ) (x+y)=2 a+(m+n-1) d- ( x+y m-n ) & S= ( m+n 2 ) [(x+y)+ x-y m-n ] aligned

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