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The consecutive odd integers whose sum is 4 5 2 - 2 1 2 are

Options

  1. A43,45, . . . . . , 75
  2. B43,45 , . . . . . , 79
  3. C43,45 , . . . . . , 85
  4. D43,45 , . . . . . , 89

Correct answer

D. 43,45 , . . . . . , 89

Step-by-step solution

Let n consecutive odd integers are 2 m + 1,2 m + 3,2 m + 5 , . . . . . , 2 m + 2 n - 1 Given that, 4 5 2 - 2 1 2 = 2 m + 1 + 2 m + 3 + 2 m + 5 + . . . . . . + 2 m + 2 n - 1 = 2 m n + 1 + 3 + 5 + . . . . . + 2 n - 1 = 2 m n + n 2 = m 2 + 2 m n + n 2 - m 2 ⇒ 4 5 2 - 2 1 2 = m + n 2 - m 2 ⇒ m + n = 45 and m = 21 ⇒ n = 24 and m = 21 Hence, the numbers are 43,45 , . . . . , 8 9

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