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The sum of (p+q)^ th and (p-q)^ th terms of an AP is equal to

Options

  1. A(2 p )^ th term
  2. B(2 q)^ th term
  3. CTwice the p ^ th term
  4. DTwice the q^ th term

Correct answer

C. Twice the p ^ th term

Step-by-step solution

Let the first term of AP = a Let the common difference of AP = d aligned & ( p + q )^ th term = T _ p + q = a +( p + q -1) d & ( p - q )^ th term =T_ p- q = a +( p - q -1) d & T _ p + q +T_ p-q = a +( p + q -1) d + a +( p - q -1) d & =2 a +( p + q -1+ p - q -1) d & =2 a +(2 p -2) d =2[ a +( p -1) d ]=2 ~T _ p aligned

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