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The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by 21 2 . Then the number of terms which are integers in the A.P. is :

Options

  1. A4
  2. B10
  3. C6
  4. D8

Correct answer

A. 4

Step-by-step solution

a ₂+ a ₄+ + a _ n =30 ...(1) a ₁+ a ₃+ + a _ n -1 =24 ...(2) (1)-(2) (a₂-a₁ )+ (a₄-a₃ ) (a_n-a_ n-1 )=6 aligned & n 2 ~d =6 nd =12 & a _ n - a ₁=( n -1) d = 21 2 & nd - d = 21 2 12- 21 2 = d & d = 3 2 , n =8 aligned aligned & Sum of odd terms = 4 2 [2 a +(4-1) 3]=24 & a = 3 2 & A.P. 3 2 , 3, 9 2 , 6, 15 2 , 9, 21 2 , 12 aligned no. of integer terms =4

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