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Sum of the first hundred numbers common to the two arithmetic progressions 12,15,18 , … … … and 17 , 21 , 25 , … … . . is

Options

  1. A56100
  2. B65100
  3. C61500
  4. D51600

Correct answer

C. 61500

Step-by-step solution

AP1 = 12 , 15 , 18 , … … . (common difference d 1 = 3 ) AP2 = 17 , 21 , 25 , … … . (common difference d 2 = 4 ) First term of the series of common numbers = 21 . Here, a = 21 , and common difference of the series of common numbers = L C M of d 1 and d 2 = 12 ⇒ Required sum of the first hundred terms = 100 2 2 × 21 + 100 - 1 12 = 100 21 + 99 × 6 = 61500

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