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NDA 2 2025 Maths, question 6

Topic: Algebra

Q6

How many terms of the series 1+3+5+7+…1+3+5+7+\ldots amount to a sum equal to 1234567898765432112345678987654321?

  1. (a) 1111111111111111
  2. (b) 110000011110000011
  3. (c) 111101111111101111
  4. (d) 111111111111111111Correct answer

Solution.

Answer: (d) 111111111111111111

  1. The sum of the first n odd positive integers is n².
  2. The given number equals 111111111², so the required number of terms is 111111111.
  3. Squaring this nine-digit repunit gives the stated symmetric sequence of digits.