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JEE Main20198 Apr 2019Morning ShiftMathematicsSequences and SeriesActual

The sum of all natural numbers n such that 100 < n < 200 and H . C . F . 91 , n > 1 is

Options

  1. A3203
  2. B3221
  3. C3121
  4. D3303

Correct answer

C. 3121

Step-by-step solution

Since,   H . C . F . of 91 ,   n > 1 . Hence, n should be multiple of 7 or 13 or both. Hence, when n is multiple of 7 , Number of terms = 14 , t 1 = 105 , l = 196 ∴ S 1 = 14 2 105 + 196 = 7 × 301 = 2107 When n is multiple of 13 , Number of terms = 8 ,   t 1 = 104 ,   l = 195 ∴ S 2 = 8 2 × 299 = 1196 When n is multiple of 91 ∴ Number of term = 1   S 3 = 182 ∴ Required sum = 2107 + 1196 - 182 = 3121

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