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The 20 th term from the end of the progression 20 , 19 1 4 , 18 1 2 , 17 3 4 , … , - 129 1 4 is :-

Options

  1. A- 118
  2. B- 110
  3. C- 115
  4. D- 100

Correct answer

C. - 115

Step-by-step solution

Given A P is 20 , 19 1 4 , 18 1 2 , 17 3 4 , . . . , - 129 1 4 . Common difference, d 1 = 19 1 4 - 20 = - 3 4 Reversing the A P such that first term becomes the last and last term becomes first. ⇒ - 129 1 4 , . . . . . . , 19 1 4 , 20 This is also A P . First term, a = - 129 1 4 and common difference, d = 3 4 . ⇒ a 20 = - 129 1 4 + ( 20 - 1 ) 3 4 ⇒ a 20 = - 517 4 + 57 4 ⇒ a 20 = - 460 4 ⇒ a 20 = - 115

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