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JEE Main201910 Apr 2019Morning ShiftMathematicsSequences and SeriesActual

If a 1 , a 2 , a 3 . . . . . . . . . , a n are in A . P . and a 1 +   a 4 + a 7 . . . . . . . . . + a 16 = 114 , then a 1 + a 6 + a 11 + a 16 is equal to :

Options

  1. A64
  2. B98
  3. C38
  4. D76

Correct answer

D. 76

Step-by-step solution

∴ We know that sum of equidistant term from end & beginning is same in any A . P . ⇒   a 1 + a 16 = a 2 + a 15 = a 3 + a 14 = a 4 + a 13 = a 5 + a 12 = … = a 7 + a 10 ∵   a 1 + a 4 + a 7 + a 10 + a 13 + a 16 = 114 ⇒ 3 a 1 + a 16 = 114 ⇒ a 1 + a 16 = 38 Then, a 1 + a 6 + a 11 + a 16 = 2 a 1 + a 16 = 76

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