Mathematical Reasoning - Number Series

11. 0, 3, 8, 15, 24, 35, 48, 63, ...

  • Option : A
  • Explanation : The series is 12 − 1, 22 − 1, 32 − 1 and so on. The next number is 92 − 1 = 80.
    Alternative solution: The differences between the numbers across the series are 3, 5, 7, 9, 11, 13, 15 and 17. The next number is 63 + 17 = 80.
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12. 2, 5, 10, 17, 26, 37, ..., 65

  • Option : A
  • Explanation : The series is 12 + 1, 22 + 1, 32 + 1 and so on. The next number is 72 + 1 = 50.
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13. 0, 2, 6, 12, 20, 30, ..., 56

  • Option : C
  • Explanation : The series is 02 + 0, 12 + 1, 22 + 2, 32 +3 and so on. The missing number is 62 +6 = 42. The next number = 62 + 6 = 42.
    First alternative solution V The series is 0 × 1,1 × 2, ....... 1 × 2, 2 × 3, 3 × 4, 4 × 5 and 5 × 6 = 30. The next number is 6 × 7 = 42.
    Second alternative solution : The series is 12 − 1, 22 − 2, 32 − 3, 42 − 4, 52 − 5, 62 − 6, 72 − 7, 82 − 8 and so on.
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14. 1, 8, 27, 64, 125, 216, ...

  • Option : B
  • Explanation : The series is 13 , 23 , 33 , etc. The missing number is 73 = 343.
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15. 2, 9, 28, 65, 126, 217, 344, ...

  • Option : A
  • Explanation : The series is 13 + 1, 23 + 1, 33 + 1 and so on. Thus, the missing number is 83 + 1 = 513.
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